Question

Cos square there + cos square theta multiply cot square theta = cot square theta​

Answer 1

Explanation:

We need to prove that : $\cos^2\theta+\cos^2\theta {\cdot} \cot^2\theta=\cot^2\theta$

Taking LHS : $\cos^2\theta+\cos^2\theta {\cdot} \cot^2\theta$

Taking $\cos^2\theta$ common as follows :

$\cos^2\theta(1+ \cot^2\theta)$ ...(1)

We know that :

$cosec^2\theta-\cot^2\theta=1\\\\cosec^2\theta=1+\cos^2\theta$ ....(2)

Use equation (2) in equation (1) as follows :

$\cos^2\theta{\cdot} cosec^2\theta$

We know that : $cosec\theta=\dfrac{1}{\sin\theta}$

So,

$\cos^2\theta{\cdot} \dfrac{1}{\sin^2\theta}\\\\=\cot^2\theta$

=RHS

Hence, LHS = RHS