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Question

The value of the expression (cosθ1)(1+cosθ)(1+cot2θ) is

A
0
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B
1
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C
sin2θ
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D
-1
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Solution

The correct option is D -1
(cosθ1)(1+cosθ)(1+cot2θ)
= (cos2θ1)(1+cot2θ)
= sin2θcosec2θ (since, sin2θ+cos2θ=1 and cosec2θcot2θ=1)
= 1

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