Question

Упростить выражение ((tg^2)*a - (sin^2)*a)*(1/sin^2a -1)

Answer 1

(tg²a - sin²a)·(1/sin²a -1) =

= ((sin²a /cos²a) - sin²a)· ((1- sin²a)/sin²a) =

= ((sin²a - sin²a ·cos²a)/cos²a)·(cos²a/sin²a) =

= (sin²a·(1 - cos²a)/cos²a)·(cos²a/sin²a) =

= (sin⁴a/cos²a)·(cos²a/sin²a) = sin²a