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Question

(i) (1 + cos θ) (1 − cos θ) (1 + cot2θ) = 1
(ii) cosec θ (1 + cos θ) (cosec θ − cot θ) = 1

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Solution

(i) LHS=(1+cosθ)(1cosθ)(1+cot2θ) =(1cos2θ)cosec2θ =sin2θ×cosec2θ =sin2θ×1sin2θ =1 =RHS(ii) LHS=cosecθ(1+cosθ)(cosecθcotθ) =(cosecθ+cosecθ×cosθ)(cosecθcotθ) =(cosecθ+1sinθ×cosθ)(cosecθcotθ) =(cosecθ+cotθ)(cosecθcotθ) =cosec2θcot2θ (cosec2θcot2θ=1) =1 =RHS

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