Prove the following trigonometric identities:\(\frac{(1+tan^2θ)cotθ}

1.	Prove the following trigonometric identities:\(\frac{(1+tan^2θ)cotθ}{cosec^2θ}\) = tanθ
Answer» \(\frac{(1+tan^2θ)cotθ}{cosec^2θ}\) = \(\frac{sec^2\times θcotθ}{cosec^2θ}\) = \(\frac{sin^2θ}{cos^2θ}\times cotθ\) = tan²θ x cotθ = tan²θ x \(\frac{1}{tanθ}\) = tanθ Hence Proved.

Prove the following trigonometric identities:\(\frac{(1+tan^2θ)cotθ}{cosec^2θ}\) = tanθ

Answer»

\(\frac{(1+tan^2θ)cotθ}{cosec^2θ}\) = \(\frac{sec^2\times θcotθ}{cosec^2θ}\)

= \(\frac{sin^2θ}{cos^2θ}\times cotθ\)

= tan²θ x cotθ

= tan²θ x \(\frac{1}{tanθ}\)

= tanθ

Hence Proved.