If $\sin x=-\frac{3}{5}$, where $\pi

Question

If $\sin x=-\frac{3}{5}$, where $\pi<x<\frac{3 \pi}{2}$, then $80\left(	an ^{2} x-\cos xight)$ is equal to\

Professor PC Thomas Classes · Answer

(a): $\sin x=\frac{-3}{5}, \pi<x<\frac{3 \pi}{2}$ $$ \cos x=\sqrt{1-\sin ^{2} x}=\sqrt{1-\frac{9}{25}}=\frac{-4}{5} $$ [ $\because x$ lies in third quadrant]\ Now, $	an x=\frac{3}{4}$\ So, $80\left(	an ^{2} x-\cos xight)=80\left(\frac{9}{16}+\frac{4}{5}ight)$ $$ =45+64=109 $$