cos2(A+B)-sin2(A-B)
{2means power}
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Answer:
Cos2ACos2B
Step-by-step explanation:
Cos²(A+B) - SIn²(A-B)
we know that Cos2A = 2Cos²A - 1 . Also Cos2A = 1 - 2Sin²A.
=> [Cos2(A+B) + 1] / 2 - [1 - Cos2(A-B)]/2
= 1/2[ Cos(2A+2B) + 1 - 1 + Cos(2A-2B)]
We know that Cos(A+B) = CosACosB + SinASinB.
Cos(A-B) = CosACosB - SinASinB
= 1/2 [ Cos2ACos2B + Sin2ASin2B + Cos2ACos2B - Sin2ASin2B]
= 2 Cos2ACos2B / 2
= Cos2ACos2B
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