Question

How do you simplify the expression `(sin^2t-tan^2t)/(tan^2tsin^2t)`?

Answer 1

= -1

Explanation:

Numerator `N = sin^2 t - sin^2t/(cos^2 t) = (sin^2 t(cos^2 t - 1))/(cos^2 t)`
Denominator `D = (sin^2 t.sin^2 t)/(cos^2 t)`
After simplification by `sin^2 t`, the expression becomes:

`N/D = (cos^2 t - 1)/(sin^2 t) = - (1 - cos^2 t)/(sin^2 t) = - sin^2 t/(sin^2 t) = -1`