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)

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)

anonymous · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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

ganeshie8 · Answer

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

anonymous · Answer

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

anonymous · Answer

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