Question

Simplify the expression sin^2 x-1/ cos(-x)

the answer choices are 
-sin x 
cos x
sin x
-cos x

Answer 1

`\hbox{using trigonometric identities:} \\ \sin^2x +\cos^2x=1 \\ \sin^2x=1-\cos^2x \\ and \\ \cos (-x)=\cos x \\ \\ (\sin^2x-1)/(\cos (-x))=(1-\cos^2 x-1)/(\cos x)=(-\cos^2x)/(\cos x)=\boxed{- \cos x} \\ (x \\ot= (\pi)/(2)+n\pi, n \in \mathbb{Z})`