Question

how do i factor

tan^2x - tan^2x sin ^2x :(

Answer 1

@AriPotta

Answer 2

?

Answer 3

tan^2 is the common factor, so factor that out first

tan^2x - tan^2x sin ^2x

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

Now replace 1-sin^2 with cos^2 (this is one of the many trig identities) to get this answer

tan^2x * cos^2x

since tan = sin/cos, we can say this

tan^2x * cos^2x

turns into

(sin^2x/cos^2x) * cos^2x

but the cosine squared terms will cancel leaving you with just sin^2x

Answer 4

so in the end, the whole expression is just sin^2x

Answer 5

where did the 1 come from in this

tan^2x(1 - sin ^2x) at the beginning

Answer 6

i factored that out, it's like saying

a - ab

is the same as

a(1 - b)

after you factor out 'a'

Answer 7

in this case, a = tan^2x and b = sin^2x