Question

Prove:
sin(90-theta)* cos(90-theta) = tan theta/ 1+ tan^2 theta

Answer 1

LHS = sin(90°-theta) × cos(90°- theta)
= cos theta × sin theta
= sin theta × cos theta


RHS = tan theta / 1 + tan^2 theta
= tan theta / sec^2 theta
= (sin theta / cos theta) × cos^2 theta
= sin theta × cos theta

Hence, LHS = RHS

Answer 2

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