Can someone help me verify this trig identity?

Question

I need to prove that

sin^2a-sin^4a=cos^2a-cos^4a.

I'm not sure what to do for the first step. If you could give me a hand with that I should be good. Thanks. <><

Answer 1

The property:

cos^2(x) + sin^2(x) = 1 is useful here.

sin^2a = 1-cos^2a

1-cos^2 a- (1-cos^2a)^2 =
1-cos^2a-1+2cos^2a - cos^4a =
cos^2a - cos^4a

Voila!

Answer 2

just use the relationship of sin^2a + cos^2a = 1.
thus sin^2a - sin^4a = (1 - cos^2a) - (1 - cos^2a)^2
then do expansion and you will get the right hand side. Thus shown!! ^-^

Answer 3

Notice that:

sin^2(a) - sin^4(a) = sin^2(a) * [1 - sin^2(a)]...same sort of thing for the other side... You should now recognize what 1 - sin^2(a) and 1 - cos^2(a) are ;)

Answer 4

Factor left side

(sina -sin^2a) - (sina + sin^2a)
(sina -[1-cos^2a]) - (sina+[1-cos^2a])
[1-cos^2a] {(sina -1) - (sina + 1)}