Question

prove

cos^4(A) - sin^4(A) =cos2A

@ganeshie8 for this, it's powers, so i can't use the previous method you hinted, right? and how can cos^4(A) - sin^4(A) = cos^2(A) - sin^2(A)

Answer 1

or if anyone else can provide an adequate explanation, that'd be cool :3

Answer 2

hint1 : a^2 - b^2 = (a+b)(a-b)

Answer 3

hint2 : sin^2A + cos^2A = 1

Answer 4

\[\large \cos^4A - \sin^2A = (\cos^2A)^2 - (\sin^2A)^2\]

Answer 5

\[\large = (\cos^2A+\sin^2A)(\cos^2A-\sin^2A)\]

Answer 6

\[\large = (1)(\cos^2A-\sin^2A)\]

Answer 7

whoa okay I got it through the hint
thank you :3