If cosec2θ (1 + cosθ)(1 - cosθ) = λ, then find the value of λ.

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

Ans: 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

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