Verify that tan2 x sin2 x tan2 x sin2 xSolutiontan2xsin2x

Verify that tan^2 x - sin^2 x = tan^2 x sin^2 x.

Solution

tan²x-sin²x= tan²xsin²x

Starting with the left side

tan²x- sin²x

sin²x/ cos²x-   sin²x

(sin²x -sin²xcos²x)/cos²x= sin²x(1-cos²x)/cos²x

                                         = sin²x* sin²x/cos²x= sin²x* tan²x