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Question

The expression E=1+cosθ+sinθ1+cosθsinθ can be simplified to


A

cosθ/(1+sinθ)

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B

(1+cosθ)/sinθ

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C

sinθ/(1+cosθ)

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D

(1-sinθ)/cosθ

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E

(1+sinθ)/cosθ

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Solution

The correct option is E

(1+sinθ)/cosθ


We multiply the numerator and denominator of E by cos θ -

E=cosθ(1+cosθ+sinθ)cosθ(1+cosθsinθ)=cosθ+sinθ.cosθ+cos2θcosθ(1+cosθsinθ)=cosθ(1+sinθ)+(1sin2θ)cosθ(1+cosθsinθ)=(1+sinθ)(cosθ+1sinθ)cosθ(1+cosθsinθ)=1+sinθcosθ


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