If `y=cos^(-1)sqrt((cos3x)/(cos^3x)),t h e ns howt h a t(dy)/(dx)=sqrt(3/(cosxcos3x))`

Explanation

\begin{equation}
\begin{aligned}
&y=\cos ^{-1}\left(\sqrt{\frac{\cos ^{3} x}{\cos ^{3} x}}\right) \\
&\cos y=\sqrt{\frac{\cos ^{3} x}{\cos ^{3} x}} \\
&=\sqrt{\frac{4 \cos ^{3} x-3 \cos x}{\cos ^{3} x}} \\
&\cos ^{2}=\sqrt{4-3 \sec ^{2} x} \\
&\cos ^{2} y=4-3 \sec ^{2} x \\
&\cos ^{2} y=4-3\left(1+\tan ^{2} x\right) \\
...