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Question

(i) (1+cosθ)(1cosθ)(1+cot2θ)=1(ii) cosecθ(1+cosθ)(cosecθcotθ)=1

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Solution

(i) (1+cosθ)(1cosθ)(1+cot2θ)=1L.H.S=(1+cosθ)(1cosθ)(1+cot2θ)=(1cos2θ)(cosec2θ)sin2θ×1sin2θ=1=R.H.S

(ii) cosecθ(1+cosθ)(cosecθcotθ)=1L.H.S=cosecθ(1+cosθ)(1sinθcosθsinθ)=cosecθ(1+cosθ)(1cosθsinθ)=(1sinθ)(1cos2θsinθ)=sin2θsin2θ=1=R.H.S


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