What is the numerical value of sin2 x cos2 x 8tan2 x sec2

What is the numerical value of -sin^2 x - cos^2 x + 8/tan^2 x - sec^2 x + 4? Express cos x + sin^2x/cos x as a single trig function.

Solution

9) ( -sin^2x -cos^2x+ 8)/( tan^2x -sec^2x +4)

use trigonemetric identity: sin^2x + cos^2x =1

1+ tan^2x = sec^2x

So, ( -sin^2x -cos^2x + 8)/( tan^2x -sec^2x +4) = ( -1 +8)/(-1 +4)

= 7/3