Question

(1+tan²θ) cot θ/cosec²θ =tan θ​

Answer 1

Answer:

I think it would be helpful to you

Answer 2

Step-by-step explanation:

We have,

$\red{\sf (1+ \tan ^2 θ) \dfrac{\cot θ}{\cosec ^2θ}= \tan θ}$

L.H.S:-

$\longmapsto\blue{\sf \sec ^2 θ \dfrac{\dfrac{\cos θ}{\sin θ} }{\cosec ^2θ}}$

$\longmapsto \blue{\sf \dfrac{1}{\cos ^2 θ} \dfrac{\dfrac{\cos θ}{\sin θ}}{\dfrac{1}{\sin ^2θ}}}$

$\longmapsto\blue{\dfrac{1}{\cos ^2 θ} \dfrac{\cos θ \sin ^2θ}{\sin θ}}$

$\longmapsto\blue{\dfrac{1}{\cos \cancel{^2} θ} \dfrac{\cancel{\cos θ} \sin ^2θ}{\sin θ}}$

$\longmapsto\blue{\dfrac{1}{\cos θ} \dfrac{\sin \cancel{^2}θ}{\cancel{\sin θ}}}$

$\longmapsto\blue{\dfrac{\sin θ}{\cos θ }}$

$\longmapsto\red{ \tan θ}$