(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 a

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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 $\sin 3A = 3\sin A - 4\sin^3 A$,we have: $= (-\cos 3A)^2 + (\sin 3A)^2$ $= \cos^2 3A + \sin^2 3A = 1$ Thus,the value of the expression is $1$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Trigonometrical ratios of multiple and sub-multiple angles

Easy

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

A
$\cos 4A$
B
$\sin 4A$
C
$1$
D
None of these

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Trigonometrical Ratios, Functions and Identities

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Trigonometrical ratios of multiple and sub-multiple angles

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DifficultIIT 1966

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

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If $\cos ^3 x \sin 4 x = \sum_{r=0}^{n} a_{r} \sin rx$ for all $x \in R$,then $a_3+a_5 : a_1+a_7 = $

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