Answer :

Given: cosec2θ (1 + cos θ) (1 cos θ) = λ

To find: λ


Consider cosec2θ (1 + cos θ) (1 cos θ)


(a – b) (a + b) = a2 – b2


cosec2θ (1 + cos θ) (1 cos θ) = cosec2 θ (1 – cos2 θ)


Now, as sin2 θ + cos2 θ = 1


sin2 θ = 1 – cos2 θ


cosec2θ (1 + cos θ) (1 cos θ) = cosec2 θ (1 – cos2 θ)


= cosec2 θ sin2 θ


Now,



cosec2 θ (1 + cos θ) (1 cos θ) = cosec2 θ (1 – cos2 θ)


= cosec2 θ sin2 θ



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