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  4. The value of (1- cos θ)(1+ cos θ)(1+ cot 2 θ) when θ= (π/15) is

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Q. The value of $(1-\cos \theta)(1+\cos \theta)\left(1+\cot ^2 \theta\right)$ when $\theta=$ $\frac{\pi}{15}$ is

TS EAMCET 2021

Solution:

$ (1-\cos \theta)(1+\cos \theta)\left(1+\cot ^2 \theta\right) $
$=\left(1-\cos ^2 \theta\right)\left(\text{cosec}^2 \theta\right) $
$ =\sin ^2 \theta \cdot \text{cosec}^2 \theta $
$=1, \forall \theta$