Question

Solve Root ( 1+ cos theta/ 1- cos theta )+ Root ( 1- cos theta/ 1 +cos theta ) = 2cosec theta ​

Answer 1

Answer:

I proved in above photo. Mark it brainlist and also our message going wide.

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Answer 2

${\underline{\underline{\frak{To\;Prove\;:}}}}$

$\sf \sqrt\frac{1 + \cos(theta) }{1 - \cos(\theta) } + \sqrt \frac{1 - \cos(\theta) }{1 + \cos(\theta) } = 2 \csc(\theta)$

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${\underline{\underline{\frak{Proof\;:}}}}$

Taking L.H.S.,

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$:\implies\sf \frac{\sqrt\frac{1 + \cos(theta) }{1 - \cos(\theta) } + \sqrt \frac{1 - \cos(\theta) }{1 + \cos(\theta) } }{(1 - \cos(\theta))(1 + \cos(\theta) ) } = 2 \csc(\theta)$

$:\implies\sf \frac{2}{ \sqrt {\sin^{2} \theta }} = 2 \csc(\theta)$

$:\implies\sf \frac{2}{ \sin \theta} = 2 \csc(\theta)$

$:\implies\sf 2 \csc(\theta) = 2 \csc(\theta)$

$:\implies\sf LHS = RHS$

$\qquad\qquad\qquad{\underline{\underline{\sf{\pink{Hence,\;Proved!}}}}}$

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$\qquad\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\: Identity\:used\:\bigstar}}}}$

• $\sf 1 - \csc^{2}\theta = \sin^{2} \theta$

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$\boxed{</p><p>\begin{minipage}{7.5 cm}</p><p> \bf \bigstar Fundamental Trigonometric Identities \\ \\</p><p> \bullet \: \: \sf \sin^2\theta + \cos^2\theta=1 \\ \\</p><p> \bullet \: \: \sf 1+\tan^2\theta = \sec^2\theta \\ \\</p><p> \bullet \: \: \sf 1+\cot^2\theta = \text{cosec}^2 \, \theta </p><p>\end{minipage}</p><p>}$