Explanation:
We need to prove that : [tex]\cos^2\theta+\cos^2\theta {\cdot} \cot^2\theta=\cot^2\theta[/tex]
Taking LHS : [tex]\cos^2\theta+\cos^2\theta {\cdot} \cot^2\theta[/tex]
Taking [tex]\cos^2\theta[/tex] common as follows :
[tex]\cos^2\theta(1+ \cot^2\theta)[/tex] ...(1)
We know that :
[tex]cosec^2\theta-\cot^2\theta=1\\\\cosec^2\theta=1+\cos^2\theta[/tex] ....(2)
Use equation (2) in equation (1) as follows :
[tex]\cos^2\theta{\cdot} cosec^2\theta[/tex]
We know that : [tex]cosec\theta=\dfrac{1}{\sin\theta}[/tex]
So,
[tex]\cos^2\theta{\cdot} \dfrac{1}{\sin^2\theta}\\\\=\cot^2\theta[/tex]
=RHS
Hence, LHS = RHS
