Question

Tan^2x-sin^2x= tan^2xsin2x

Buktikan identitas trigonometri ini

Answer 1

Tan^2x - sin^2x = sin^2x/cos^2x - sin^2x
= sin^2x/cos^2x - (sin^2xcos^2x)/cos^2x
= (sin^2x - sin^2xcos^2x)/cos^2x
= (sin^2x(1 - cos^2x))/cos^2x
= (sin^2x.sin^2x)/cos^2x
= sin^2x/cos^2x * sin^2x
= tan^2x.sin^2x
Q.E.D.