how to simplify tan squared X- sin squared X to tan squared X times sin squared X
I guess we have
[ tan^2x - sin^2x ] / [ tan^2x * sin^2x ] =
[ sin^2x / cos^2x - sin^2x] / [ sin^2x * sin^2x / cos^2x ] =
[sin^2x ( 1/cos^2x - 1 ) ] / [ sin ^2x * (sin^2x / cos^2x ) ] =
[ sec^2 x - 1 ] / [ sin^2x / cos^2x ] =
tan^2x / tan^2x =
1
how to simplify tan2 x - sin2x to tan2x * sin2x
tan2 x - sin2x
= sin2x / cos2x - sin2x cos2x / cos2x
= [ sin2x - sin2x cos2x ] / cos2x
= [ sin2x ( 1 - cos2x ) ] / cos2x
= [ sin2x (sin2x) ] / cos2x
= sin2x / cos2x * sin2x
= tan2x * sin2x