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Question

The value of cotθ+cosecθ1cotθcosecθ+1 is

A
1+cosθsinθ
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B
1+sinθsinθ
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C
1cosθsinθ
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D
1sinθsinθ
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Solution

The correct option is A 1+cosθsinθ
cotθ+cosecθ1cotθcosecθ+1=(cotθ+cosecθ)(cosec2θcot2θ)cotθcosecθ+1=(cotθ+cosecθ)(cotθ+cosecθ)(cotθcosecθ)cotθcosecθ+1=(cotθ+cosecθ)(cotθcosecθ+1)cotθcosecθ+1=cotθ+cosecθ=cosθsinθ+1sinθ=1+cosθsinθ

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