Question

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

Answer 1

`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