The value of cos2⁡A3−4cos2⁡A2+sin2⁡A3−4sin2⁡A2 is equal to

Solution:

$\begin{array}{l} \cos^{2} A {(3 - 4 \cos^{2} A)}^{2} + \sin^{2} A {(3 - 4 \sin^{2} A)}^{2} \\ = {(3 \cos A - 4 \cos^{3} A)}^{2} + {(3 \sin A - 4 \sin^{3} A)}^{2} \\ = (- \cos 3 A)^{2} + (\sin 3 A)^{2} = 1 \end{array}$

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