Question

Simplify the expression.
(cos^2 x + sin^2 x)/(cot^2 x-csc^2 x)

Answer 1

it's basic that you have to know, sin^2x + cos^2x = 1

so
(sin^2x + cos^2x) - (csc^2x - cot^2x) = 1 - ((1/sin^2x) - (cos^2x/sin^2x))
= 1 - ((1 - cos^2x)/sin^2x)
= 1 - (sin^2x/sin^2x)
= 1 -1 = 0

Answer 2

-1