Find the value of cosecθ (1 − cosθ) (cosecθ + cotθ).
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Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1.
cosecθ(1 - cosθ)(cosecθ + cotθ)
= (cosecθ - cosecθ.cosθ)(cosecθ + cotθ)
= (cosecθ - 1/sinθ × cosθ)(cosecθ + cotθ), since [cosecθ = 1/sinθ]
= (cosecθ - cotθ)(cosecθ + cotθ), since [cosθ/sinθ = cotθ]
= cosec2θ - cot2θ, since [1 + cot2θ = cosec2θ]
= 1