cos^2 A(3 - 4cos^2 A)^2 + sin^2 A(3 - 4sin^2 | vedclass

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(C) Given expression: $\cos^2 A(3 - 4\cos^2 A)^2 + \sin^2 A(3 - 4\sin^2 A)^2$$= (3\cos A - 4\cos^3 A)^2 + (3\sin A - 4\sin^3 A)^2$Using the triple ang

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(C) Given expression: $\cos^2 A(3 - 4\cos^2 A)^2 + \sin^2 A(3 - 4\sin^2 A)^2$$= (3\cos A - 4\cos^3 A)^2 + (3\sin A - 4\sin^3 A)^2$Using the triple angle identities: $\cos 3A = 4\cos^3 A - 3\cos A$ and $\sin 3A = 3\sin A - 4\sin^3 A$.Note that $(3\cos A - 4\cos^3 A)^2 = (-(4\cos^3 A - 3\cos A))^2 = (-\cos 3A)^2 = \cos^2 3A$.So,the expression becomes $\cos^2 3A + \sin^2 3A$.Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we get $\cos^2 3A + \sin^2 3A = 1$.Trick: Substitute $A = 0^\circ$. The expression becomes $\cos^2 0(3 - 4\cos^2 0)^2 + \sin^2 0(3 - 4\sin^2 0)^2 = 1(3 - 4)^2 + 0 = (-1)^2 = 1$.

$\cos^2 A(3 - 4\cos^2 A)^2 + \sin^2 A(3 - 4\sin^2 A)^2 = $

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