Question

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

Answer 1

Step-by-step 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=(1)/(\sin\theta)`

So,

`\cos^2\theta{\cdot} (1)/(\sin^2\theta)\\\\=\cot^2\theta`

=RHS

Hence, LHS = RHS