Question

If cosec² θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ. 

Answer 1

Given: 

`cosec^2θ (1+cosθ)(1-cosθ)=λ` 

⇒ `cosec^2θ (1+cosθ)(1-cosθ)=λ`  

⇒ `cosec^2θ(1-cos^2θ)=λ` 

⇒`cosec^θ sin^2θ=λ`

⇒`1/sin^2θxx sin^2θ=λ` 

⇒` 1=λ`

⇒`λ=1`

Thus, the value of λ is 1.