Question

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

Answer 1

use the difference square formula to simplifying the letf side.
a^2 - b^2 = (a-b)(a+b)

Answer 2

Would this be right then for LS? (cosx - sinx)(cosx + sinx) ?

Answer 3

so,
cos^4(x) - sin^4(x)
= (cos^2(x) - sin^2(x)) (cos^2(x) + sin^2(x)
= (cos^2(x) - sin^2(x))

then use the identity ;
cos^2 (x) = 1 - sin^2 (x)

therefore,

(cos^2(x) - sin^2(x))
= 1 - sin^2 (x) - sin^2 (x)
= 1 - 2sin^2(x)

Answer 4

what did you do from
= (cos^2(x) - sin^2(x)) (cos^2(x) + sin^2(x)
= (cos^2(x) - sin^2(x))

Answer 5

this is an identity also, cos^2 x + sin^2 = 1
(cos^2(x) - sin^2(x)) (cos^2(x) + sin^2(x)
= (cos^2(x) - sin^2(x)) * 1
= (cos^2(x) - sin^2(x))

Answer 6

Ah I see ok great!