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B
1+sinθsinθ
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C
1−cosθsinθ
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D
1−sinθsinθ
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Solution
The correct option is A1+cosθsinθ cotθ+cosecθ−1cotθ−cosecθ+1=(cotθ+cosecθ)−(cosec2θ−cot2θ)cotθ−cosecθ+1=(cotθ+cosecθ)−(cotθ+cosecθ)(cotθ−cosecθ)cotθ−cosecθ+1=(cotθ+cosecθ)(cotθ−cosecθ+1)cotθ−cosecθ+1=cotθ+cosecθ=cosθsinθ+1sinθ=1+cosθsinθ