Prove the identity sin2 x 1sec2 x 1 sin2 xSolutionsin2x 1

Prove the identity. (sin^2 x - 1)(sec^2 x - 1) = -sin^2 x

Solution

(sin²x -1)(sec²x -1)

=(cos²x)(-tan²x)........................................[since sin²x+cos²x =1, sec²x -tan²x =1]

=(cos²x)(-sin²x_/cos²x)................................[tanx =sinx_/cosx]

=-sin²x