The value of $x$ such that $\sin \left(2 an ^{-1} \frac{3}{4} ight)=\cos \left(2 an ^{-1} x ight)$ is

Question

The value of $x$ such that $\sin \left(2 	an ^{-1} \frac{3}{4}ight)=\cos \left(2 	an ^{-1} xight)$ is

Aicharya · Accepted Answer

$\begin{aligned} & \sin \left(2 	an ^{-1} \frac{3}{4}ight)=\cos \left(2 	an ^{-1} xight) \ & \Rightarrow \frac{2 	imes \frac{3}{4}}{1+\left(\frac{3}{4}ight)^2}=\frac{1-x^2}{1+x^2}=\frac{24}{25} \ & \Rightarrow 25-25 x^2=24+24 x^2 \Rightarrow 49 x^2=1 \Rightarrow x=\frac{1}{7}\end{aligned}$

The value of $x$ such that $\sin \left(2 \tan ^{-1} \frac{3}{4}\right)=\cos \left(2 \tan ^{-1} x\right)$ is

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