How to factor and simplify the expression 4tan^2x-4tan^2xsin^2x using fundamental identities?

1 Answer
Oct 29, 2017

4sin^2x

Explanation:

4tan^2x - 4tan^2xsin^2x

Hmmm. well, you can factor out 4tan^2x, giving:

4tan^2x(1 - sin^2x)

...since sin^2x + cos^2x = 1, then 1 - sin^2x = cos^2x

So you can rewrite the expression as:

4tan^2xcos^2x

...then, you can rewrite tan^2x as sin^2x/cos^2x, so this makes your expression:

4sin^2x/cos^2x * cos^2x

...and the 2 cos^2x terms cancel, leaving:

4sin^2x

...which I think may be the best you can do.

GOOD LUCK