if tano+sino = m,tano -sino =n,prove that m² -n²=4root mn

How to make working model on trigonometry?

if cos theta + sin theta =root2 cos theta prove that cos theta - sin theta =root 2 sin theta

 If a sin theta + b cos theta = c , then prove that a cos theta - b sin theta = the whole under root a² + b² - c² . 

plz answer soon if u want a thumbzzzz up guys !!!!!!!!!!!!!

if secA =x+ (1/4x), prove that secA + tanA =2x or 1/2x

rply fst!!!

if tan theta +sin theta=m, tan theta -sin theta=n show that m square -n square=4 root mn

a person had a number of toys to distribute among children . at first he gave 2 toys to each child , then 4 , then 5 ,and then 6 , but was always left with one . but if he had given 7 toys to each child , no toys would have been left with him . what is the smallest number of toys that he had?

prove that tan theta/1-cot theta +cot theta/1-tan theta=1+tan theta+cot theta

Plzz answer fast

If sec(theta)=x+1/4x, prove that sec(theta)+tan(theta)=2x or 1/2x

please answer my ques. Thanks in advance.

If ^{cos(theta) - sin(theta)}/ _{cos(theta) + sin(theta)} = ^{1 - (root)3} / _{1 + (root)3}

Find (theta)

if a+b=90. prove that root of tana.tanb + tana.cotb / sina .secb - root of sin²b / cos²a=tana

Prove that sin theta-cos theta+1/sin theta+cos theta-1 = 1/sec theta -tan theta.

if the pair of equations x + y = root 2. and x sin A + y cos A = 1 has infinitely many solutions, then A = ?

options : 30, 45, 60 and 90

 find the value of sin30 geometrically

Find the value of sec45 geometrically. Hence find sin 45 and cos 45 ?

if sec theta+tan theta =p ,prove that sin theta = (p square- 1) / (p square + 1)

tanA + secA -1 / tanA - secA + 1=1+sinA / cosA

Prove That: cos³theta+ sin³theta/cos theta+sintheta

+cos³theta-sin³theta/costheta-sintheta

if A,B,c are interior angles of triangle ABC then show that sin (B+C/2) = cos A/2

Find the value of sin60 geometrically

If acosx-bsinx =c, prove that asinx + bcosx = +- root(a²+b²-c²)

find the value of sin 30 and sin 60 , geometrically .

If cosec theta - cot theta = 1/3 then find the value of ( cosec theta + cot theta)

de value of cos1 cos2 cos 3 ....cos 180 is =?

plz answer!!!

If sec (theta) + tan (theta) = 7 then find the value of sec (theta) - tan (theta)

cosA - sinA + 1 / cosA + sinA - 1 = cosecA + cotA

If x/a cos theta+y/b sin theta=1 and x/a sin theta-y/b cos theta=1, prove that x square/a square+y square/b square=2

Dear Expert

Kindly assist to solve the following problems:

1. If Cot Theta =2, Find the values of all other Trigonometric Ratios Theta.

2. If 5 Cot Theta = 3, Evaluate 5 Sin Theta - 3 Cos Theta / 5 Sin Theta + 3 Cos Theta.

3. Evaluate Tan²60 + 4 Cos²45 + 8 Cosec²60 / 2 Cosec 30 +3 Sec 60 + 7/3 Cot²30.

4. Evaluate (Cosec²(90 - Theta) - Tan²Theta/ 4(Cos²48 +Cos²42)) - ( 2Tan²30 x Sec²52 x Sin²38 / Cosec² )

5. (Sin Theta -Cos Theta + 1 / Sin Theta + Cos Theta -1)=1 / Sec Theta - Tan Theta.

REQUESTAN URGENT REPLY, PLEASE.

Express sin theta in terms of sec theta.

 if  root 3 tan theta = 3 sin theta, then ( sin² thea - cos² theta) = ??

if sin theta - cos theta = 1/2, find the value of sin theta+ cos theta

prove that

(1+cot theta -cosec theta ) (1+ tan theta + sec theta) =2

if cosA +sinA=root2cosA show that cosA -sinA=root2 sina

an equilateral triangle is inscribed in a cirle of radius 6 cm.Find its sides

Here are few questions from the chapter Introduction to Trigonometry for practise:- 1. In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine a. sin A, cos A b. sin C, cos C 2. Given 15 cot A = 8. Find sin A and sec A 3. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B. 4. In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P. 5. State whether the following are true or false. Justify your answer. a. The value of tan A is always less than 1.. b. cos A is the abbreviation used for the cosecant of angle A. c. cot A is the product of cot and A 6. Evaluate the following a. sin60° cos30° + sin30° cos 60° b. 2tan245° + cos230° − sin260° 7. State whether the following are true or false. Justify your answer. a. sin (A + B) = sin A + sin B b. The value of sinθ increases as θ increases c. The value of cos θ increases as θ increases d. sinθ = cos θ for all values of θ e. cot A is not defined for A = 0° 8. Show that tan 48° tan 23° tan 42° tan 67° = 1 cos 38° cos 52° − sin 38° sin 52° = 0 9. If tan 2A = cot (A− 18°), where 2A is an acute angle, find the value of A. 10. If tan A = cot B, prove that A + B = 90° 11. If sec 4A = cosec (A− 20°), where 4A is an acute angle, find the value of A. 12. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°. 13. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. 14. : Write all the other trigonometric ratios of ∠A in terms of sec A. 15. Prove the following identities, where the angles involved are acute angles for which the expressions are defined. 16. (sec2q -1 ) (1 - cosec2q )=…………… 17. cot2q– 1/ Sin2q = ............................ 18. Given that sinq =a/b , then cos q is equal to -------------------- 19. If sin q - cos q = 0 , then the value of (sin4q + cos4q) is ……………. 20. Eualuate(1 + cot q - cos q)(1 + tanq + sec q) 21. If x = a sec q cos Ø ; y = b sec q sin Ø and z = c tan q , then X2 / a2 + Y2 /b = ………………. 22. If cosA +cos2 A = 1, then sin2 A + sin2A= 23. Prove that sec 72/ cos ec18 + sin59/ cos31 = 2 24. If sin 2 q = √3 , find q 25. Prove that cos q - sin q =√ 2 sin q,if sin q + cos q = √2 cos q 26. Prove that (tanA+ secA- 1) / (tanA-secA + 1) = secA + tanA 27. If a cos3 q + 3 cos q sin2q = m a sin3q + 3acos2q sinq = n, 28. Prove that(m+ n)2 /3+ (m+ n)2/3= 2a 2 /3 29. If 1 secq = x + 1/4x prove that sec q + tan q = 2x or 1/2x 30. If √3 tan q = 3 sinq , evaluate sin2q - cos2q 31. Prove the following identities : 1+ sec A/SecA = sin2 A/1 - cos A 32. Prove that : 1/ secq - tanq - 1/ cosq = 1/cosq -1/ secq + tanq 33. Prove the following identity: (sin A + cosec A)2 + ( cos A + sec A )2 = 7 + tan2A + cot2A. 34. If x/a cos = y/bsin and ax/cos = by/sin = a2 –b2 prove that x2 /a2 + y2 /b2 35. If cotA =4/3 check (1 – tan2A)/ 1 + tan2A = cot2A – sin2A 36. sin (A – B) = ½, cos(A + B) = ½ find A and B 37. Evaluate tan5° tan25° tan30° tan65° tan85° 38. Verify 4(sin430° + cos 460°) – 3(cos245° – sin290°) = 2 39. Show that tan48° tan23° tan 42° tan67° = 1 40. sec4A = cosec(A – 20) find A 41. tan A = cot B prove A + B = 90 42. A, B, and C are the interior angles of DABC show that sin( B + C )/2 = cos A/2 43. In DABC, if sin (A + B – C) = √3/2 and cos(B + C – A) =1/√2, find A, B and C. 44. If cos θ = and θ + φ = 900, find the value of sin φ. 45. If tan 2A = cot ( A – 180 ), where 2A is an acute angle, find the value of A. 46. If 2sin (x/2) = 1 , then find the value of x. 47. If tan A = ½ and tan B = 1/3 , by using tan (A + B) = ( tan A + tan B )/ 1 – tan A. tan B prove that A + B = 45º 48. Express sin 76° + cos 63° in terms of trigonometric ratios of angles between 0° and 45°. 49. Prove that: 2 sec2 θ – sec4 θ – 2 cosec2 θ + cosec4 θ = cot4 θ – tan4 θ 50. Find the value of θ for which sin θ – cos θ = 0 51. Given that sin2A + cos2A = 1, prove that cot2A = cosec2A – 1 52. If sin (A + B) = 1 and sin (A – B)=1/2 0o< A + B ≤ 90o; A > B, find A and B. 53. Show that tan 620/cot 280 =1 54. If sin A + sin2A = 1, prove that cos2A + cos4A = 1. 55. If sec 4A = cosec (A – 200), where 4A is an acute angle, find the value of A. 56. Prove that (cosec θ – sec θ) (cot θ – tan θ) = (cosec θ + sec θ) (sec θ . cosec θ – 2) 57. Given that A = 60o, verify that 1 + sin A =(Cos A/2 + Sin A/2)2 58. If sin θ + cos θ = x and sin θ – cos θ = y, show that x2 + y2 = 2 59. Show that sin4θ – cos4θ = 1 – 2 cos2θ 60. If θ= 45o. Find the value of sec2θ 61. Evaluate: cos60 o cos45 o -sin60 o sin45 o 62. Find the value of tan15 o.tan25 o.tan30 o tan65 o tan85 o 63. If θ is a positive acute angle such that sec θ = cosec60o, then find the value of 2cos2 θ -1 64. Find the value of sin65-cos25 without using tables. 65. If sec5A=cosec(A-36 o). Find the value of A. 66. If 2 sin x/2 - 1 =0, find the value of x. 67. If A, B and C are interior angles of ΔABC, then prove that cos (B+C)/2 = sinA/2 68. Find the value of 9sec2A-9tan2A. 69. Prove that sin6θ+cos6θ=1-3sin2θcos2θ. 70. If 5tanθ-4=0, then find the value of (5sinθ - 4cosθ) (5sinθ + 4cosθ) 71. In ABC, <c=90o, tan A= and tan B=<3.Prove that sin A. cos B+ cos A .sin B=1. 72. In D ABC, right angled at B, if tan a =1/√3 find the value of Sin A cos C + cos A sin C. 73. Show that 2(cos4 60 + sin4 30 )- (tan2 60 + cot2 45 ) + 3sec2 30 =1/4 74. sin(50 +q ) - cos(40 -q ) + tan1 tan10 tan 20 tan 70 tan80 tan89 =1 75. Given tan A =4/3, find the other trigonometric ratios of the angle A. 76. In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1. 77. In D OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm. Determine the values of sin Q and cos Q. 78. In D ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:(i) sin A , cos A(ii) sin C, cos C 79. If ÐA and ÐB are acute angles such that cos A = cos B, then show that Ð A = ÐB. 80. If cot A= 7/8 evaluate: {(1 + sinA )( 1 – sinA)} / {(1+ cosA)(1-cosA) 81. In triangle ABC, right-angled at B, if tan A = 1/√3 find the value of :(i) sin A cos C + cos A sin C (ii) Cos A cos C – sin A sin C 82. In D ABC, right angled at B, AB = 5 cm and ÐACB = 300 Determine the lengths of the sides BC and AC. 83. In D PQR, right – angled at Q, PQ = 3 cm and PR = 6 cm. Determine ÐQPR and ÐPRQ 84. If sin (A-B) = ½ ,cos(A+B ) = ½ A+ B = o < A+ B ≤ 90, A > B find A and B 85. Evaluate the following: (5cos260 + 4sec230 - tan2 45)/ (sin2 30 + cos2 30) 86. If sin 3 A = cos (A – 26), where 3 A is an acute angle, find the value of A. 87. Prove the trigonometric identities (1 - cos A)/( 1 – cos A) = (cosec A – cot A)2 88. Prove the trigonometric identities ( 1+ 1/tan2A) (1 + 1/cot2A) = 1/(sin2A- cos4A) 89. Prove the trigonometric identities (sec4A – sec2A) = tan4A +tan2A = sec 2 A tan2 A 90. Prove the trigonometric identities cotA – tanA = (2cos 2A -1)/ (sinA.cosA) 91. Prove the trigonometric identities.(1- sinA +cosA)2 = 2(1+cosA )(1 – sinA) 92. If tanA +sinA = m and tanA – sinA=n show that m2 – n2 = 4 93. If x= psecA + qtanA and y= ptan A +q secA prove that x2 – y2 = p2 – q2 94. If sinA + sin2A = 1 prove that cos2 A + cos4 A =1 95. Express the following in terms of t-ratios of angles between 0° and 45°. 1) sin 85° +cosec 85° 2) cosec 69° +cot 69° 3) sin 81° +tan 81° 4) cos 56° +cot 56° 96. [sin (90 -A) sin A]/tan A-1 = - sin² A 97. cos cos(90° - ) -sin sin (90° - ) = 0 98. sin (90° - ) cos (90° - ) = tan /(1 +tan² ) 99. cosec² (90° - ) -tan² = cos²(90° - ) +cot² 100. If cos /cos = m and cos /sin = n, show that (m² +n²) cos² = n².If x = r cos sin , y = r cos cos and z = r sin , show that x² +y² +z² = r².

prove that 1/sec theta -tan theta - 1/cos theta=1/cos theta-1/sec theta + tan theta

prove sin theta-2sin cube theta/2cos cube theta-cos theta=tan theta

 solve (cosec theta-sin theta)(sec theta - cos theta) = 1tan theta + cot theta

The following questions are based on the given data for an examination.

A. Candidates appeared 10500
B. Passed in all the five subjects 5685
C. Passed in three subject only 1498
D. Passed in two subject only 1250
E. Passed in one subject only 835
F. Failed in English only 78
G. Failed in maths only 275
H. Failed in Physics only 149
I. Failed in chemistry only 147
J. Failded in Biology only 221

Correct Answer : (D)

Your Answer : (A)

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Correct Answer : (A)

Your Answer : (B)

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Correct Answer : (B)

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Correct Answer : (C)

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If cosec theta + cot theta= p Prove that cos theta = p²-1 by p²+1

Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.

(1+ cot A - cosec A) (1+ tan A + sec A) = 2

cos45 degree divided by sec 30 degree plus cosec 30 degree .... hw do u solve it in simple way ... nd hw do v rationalise d denominator

prove that tan+sec-1/tan-sec+1 =1+sin/cos

Prove that:- sin⁶ theta + cos⁶ theta = 1-3sin²theta.cos²theta

10. If Sin + Cos = p and Sec + Cosec = q, show that q(p2 – 1) = 2p.

prove that cotA + cosecA -1/ cotA - CosecA + 1 = 1 + cosA - sinA

if A and b are acute angles such that cosA=cosB, then show that ANGLEA=ANGLEB.

if 1+ sin²A = 3sinAcosA, then show that tanA =1or 1/2. plzzzzz urgen 2mrow is my exam

given that sin theta + 2 cos theta = 1 , then prove that 2 sin theta -cos theta = 2

if sin 3 theta = cos ( theta-6 degree) where 3 theta and ( theta-6 degree) both r acute angle then what is the value of theta

if sec theta+tan theta=m,then tan theta is equal to.

tanA / 1-CotA + CotA / 1-TanA = 1 + TanA + Cot A

1 +( cot²A /1 + cosecA)=cosecA

cosA /1-tanA +sinA / 1-cotA =sinA+cosA

 prove that 1/ secA+tanA - 1/cosA = 1/cosA - 1/ secA- tanA

if cosec A+Cot A= p , then proove that cOS A = p2 - 1 / p2+ 1

If sec A = x + 1/4x then prove that tan A + secA = 2x or 1/2x