If cosecA - cotA = q , then show that q2 -1/q2 +1 +cosA=0 - Maths - Introduction to Trigonometry

Question

If cosecA - cotA = q , then show that q2
-1/q2 +1 +cosA=0

Manbar Singh · Accepted Answer

We have, q = cosec A - cot A⇒q2 = cosec A - cot A2⇒q2 =
cosec2A + cot2A - 2 cosec A cot A⇒q2 = 1sin2A + cos2Asin2A -
2 cos Asin2A⇒q2 = 1 + cos2A - 2 cos A sin2A⇒q2 = 1 -
cos A21 - cos2A = 1-cos A1 - cos A1 - cos A1 + cos A = 1 - cos A1 +
cos ANow,LHS = q2-1q2+1 + cos A=1 - cos A1 + cos A - 11-cos A1 +
cos A + 1 + cos A=1 - cos A - 1 - cos A1 - cos A + 1 + cos A + cos
A=-2 cos A2 + cos A= - cos A + cos A=0=RHS