If sin x = - 3/4, where π < x< 3π/2, then 80(tan^2 x – cosx) is equal to :

Question

If \(\sin x=-\frac{3}{5}\), where \(\pi<x<\frac{3 \pi}{2}\), then 80(tan² x – cosx) is equal to :

(1) 109 

(2) 108 

(3) 18 

(4) 19

Answer 1

Correct option is (1) 109   

\(\sin x=\frac{-3}{5}, \pi<x<\frac{3 \pi}{2}\)

\(\tan x=\frac{3}{4} \cos x=-\frac{4}{5}\)

\(80\left(\tan ^{2} x-\cos x\right)\)

\(=80\left(\frac{9}{16}+\frac{4}{5}\right)=45+64=109\)