Solve 2 tan ^{-1}(cos x)=tan ^{-1}(2 csc x) | vedclass

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(A) Given equation: $2 	an ^{-1}(\cos x)=	an ^{-1}(2 \csc x)$Using the formula $2 	an ^{-1} 	heta = 	an ^{-1} \left( \frac{2 	heta}{1 - 	heta^2

Vedclass · Accepted Answer

$x=\frac{\pi}{4}$

Vedclass · Answer

(A) Given equation: $2 	an ^{-1}(\cos x)=	an ^{-1}(2 \csc x)$Using the formula $2 	an ^{-1} 	heta = 	an ^{-1} \left( \frac{2 	heta}{1 - 	heta^2} ight)$,we get:$	an ^{-1} \left( \frac{2 \cos x}{1 - \cos^2 x} ight) = 	an ^{-1} (2 \csc x)$Equating the arguments:$\frac{2 \cos x}{\sin^2 x} = 2 \csc x$Since $\csc x = \frac{1}{\sin x}$:$\frac{2 \cos x}{\sin^2 x} = \frac{2}{\sin x}$Assuming $\sin x 
eq 0$,we can cancel $2$ and one $\sin x$ from both sides:$\frac{\cos x}{\sin x} = 1$$\cot x = 1$$	an x = 1$Therefore,$x = \frac{\pi}{4}$.

Solve $2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \csc x)$

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