i have 2 question -

1)if cos -1 (x/a)+cos-1(y/b)=d

prove that : x2/a2-2xy/ab-cosd+y2/b2=sin2d

2)solve tan(cos-1x)=sin(tan-1x)

3)tan-1x+tan-1y+tan-1z=pi/2

prove that xy+yz+zx =1

 

Dear Student, in future please ask questions separately and not together. Thanks

  • 104

 cos -1 (x/a)+cos-1(y/b)=d

cos -1 (x/a) =d - cos-1(y/b

Taking cos on both sides:

 (x/a)= cos(d - cos-1(y/b)

(x/a)= cosd cos(cos-1(y/b) +sind sin(cos-1(y/b))

x/a= cosd y/b +sind(root of 1- (y/b)2

x/a- y/bcosd= sind(root of 1-(y/b)2                                                            

squaring on both sides,                                                           (sin (cos-1X = ROOT OF 1- X^2))

x2/a2  + y2 / b2 cos2 d -2 xy cosd/ab= sin2 d  -  sin2 d y2/b2  

x2/a2  + y/ b2( cos2 d + sin2 d) -2 xy cosd/ab =  sin2 d                  (cos2 d + sin2 d= 1)

x2/a2  + y/ b2 -2 xy cosd/ab=  sin2 d

  • 26

thank you harshini good answer

  • -3
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