$ an \left(\cos ^{-1} \frac{1}{\sqrt{2}}+ an ^{-1} \frac{1}{2} ight)=$

Question

$	an \left(\cos ^{-1} \frac{1}{\sqrt{2}}+	an ^{-1} \frac{1}{2}ight)=$

Aicharya · Accepted Answer

$	an \left(\cos ^{-1} \frac{1}{\sqrt{2}}+	an ^{-1} \frac{1}{2}ight)$ Let $	heta=\cos ^{-1} \frac{1}{\sqrt{2}}$ and $\phi=	an ^{-1} \frac{1}{2}$ $\begin{aligned} & 	herefore \quad \cos 	heta=\frac{1}{\sqrt{2}} 	ext { and } 	an \phi=\frac{1}{2} \ & 	herefore \quad 	an 	heta=1 \ & \quad 	ext { Given expression }=	an (	heta+\phi) \ &=\frac{	an 	heta+	an \phi}{1-	an 	heta 	an \phi} \ &=\frac{1+\frac{1}{2}}{1-\frac{1}{2}}=3 \end{aligned}$

$\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)=$

Solution