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Question

Choose the correct option:
(cosec θ+cot θ)×(1cos θ)=


A

cot θ

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B

sec θ

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C

sin θ

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D

cosec θ

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Solution

The correct option is C

sin θ


cosec θ=1sin θ, cot θ=cos θsin θ

When we rationalise (1cos θ), we get,

(1sin θ+cos θsin θ)×(1cos θ)×(1+cos θ)(1+cos θ)=(1+cos θ)sin θ×(1cos2θ)(1+cos θ).
After simplifying we get (1cos2θ)sin θ. Now 1cos2θ=sin2θ on further simplifying,
sin2θsin θ=sin θ


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