Q) If $\csc^2\theta (1 + \cos \theta) (1 - \cos \theta)$ = λ, then find the value of λ.

Solving LHS LHS = $\csc^2\theta (1 + \cos \theta) (1 - \cos \theta)$ $\frac{1}{\sin\^2\theta} (1 - \cos^2 \theta)$ ............ (i) We know that $\sin^2\theta + \cos^2\theta$ = 1 ∴ $1- \cos^2\theta = \sin^2 \theta$ By substituting this value in equation (i) , we get: $\frac{1}{\sin\^2\theta} (1 - \cos^2 \theta)$ = $\frac{1}{\sin\^2\theta} (\sin^2 \theta)$ = 1 Since RHS = λ Therefore λ = 1 https://youtube.com/shorts/D4u5zzp6OTg