prove the identities?

Question

Prove the identities?
1) cos^6 + sin^6 = 1-3sin^2x +3sin^4x
2)tan(x+y)tan(x-y) = (sin^2x- sin^2y)/(cos^2x-sin^2x)
3)sin(5x) = sinx[ cos^2(2x) - sin^2 (2x)] + 2 cosx cos(2x)sin(2x)
4) sin^2 + cos^4 = cos^2+sin^4

Answer 1

To show these identities are equal you must modify one side of the equation to look like the other.
By simply looking at them I think you should be simplifying them with the pythagorean identities and the half-angle formulas possibly.
The most helpful I have found through hard won experience is sin^2+cos^2=1

Good luck!

Answer 2

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

Answer 3

you don't prove identities, you verify them. Start with one side of the statement and work it through until you come up with the other side. You can't treat them as equations, that is what you are trying to show. Use the sum and difference identities and so forth to work the one side.

Answer 4

just simplify with trigonometric
here's the function as well

Answer 5

elevendy-four to the second power squared over easy

Anymore brain busters?