If cos ,x = frac{{2cos y - 1}}{{2 - cos | vedclass

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Question

Given $\cos x=\frac{2 \cos y-1}{2-\cos y}$

Applying compoundo and dividendo rule

$\frac{1+\cos x}{1-\cos x}=\frac{2 \cos y-1+2-\cos y}{2-\cos y-

Vedclass · Accepted Answer

$\sqrt 3$

Vedclass · Answer

Given $\cos x=\frac{2 \cos y-1}{2-\cos y}$

Applying compoundo and dividendo rule

$\frac{1+\cos x}{1-\cos x}=\frac{2 \cos y-1+2-\cos y}{2-\cos y-2 \cos y+1}$

$\Longrightarrow \frac{2 \cos ^{2} x / 2}{2 \sin ^{2} x / 2}=\frac{1+\cos y}{3(1-\cos y)}=\frac{\cos ^{2} y / 2}{3\left(2 \sin ^{2} y / 2ight)}$

$\Longrightarrow 	an ^{2} \frac{x}{2}=3 	an ^{2} \frac{y}{2}$

$\Longrightarrow 	an \frac{x}{2} \cot \frac{y}{2}=\sqrt{3}$

If $\cos \,x = \frac{{2\cos y - 1}}{{2 - \cos y}},x,\,y\, \in \,\left( {0,\pi } \right),$ then $tan(x/2)cot(y/2) =$

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