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Question

Question: \[\sin(\pi + \theta)\sin(\pi - \theta)\text{ cose}\text{c}^{2}\theta =\]...

sin⁡(π+θ)sin⁡(π−θ) cosec2θ=\sin(\pi + \theta)\sin(\pi - \theta)\text{ cose}\text{c}^{2}\theta =

A

1

B

–1–1

C

sin⁡θ\sin\theta

D

−sin⁡θ- \sin\theta

Answer

–1–1

Explanation

Solution

sin⁡(π+θ)sin⁡(π−θ)cosec2θ=−sin⁡θsin⁡θ1sin⁡2θ=−1\sin(\pi + \theta)\sin(\pi - \theta)\text{cose}\text{c}^{2}\theta = - \sin\theta\sin\theta\frac{1}{\sin^{2}\theta} = - 1.