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Question

(1+cot2θ)(1cosθ)(1+cosθ)=

A
tan2θsec2θ
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B
sin2θcos2θ
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C
sec2θtan2θ
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D
cos2θsin2θ
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Solution

The correct option is D sec2θtan2θ
We have,
(1+cot2θ)(1cosθ)(1+cosθ)

(1+cot2θ)(1cos2θ) a2b2=(a+b)(ab)

(1+cot2θ)(sin2θ) sin2θ=1cos2θ

(csc2θ)(sin2θ) 1+cot2θ=csc2θ

1sin2θ×sin2θ csc2θ=1sin2θ

1

sec2θtan2θ sec2θtan2θ=1

Hence, this is the answer.

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