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

cos 4 A

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sin 4 A

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1

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N o n e o f t h e s e

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Solution

The correct option is C $1$
${cos}^{2} A (3 - 4 {cos}^{2} A)^{2} + {sin}^{2} A (3 - 4 {sin}^{2} A)$
$\Rightarrow (3 cos A - 4 {cos}^{3} A)^{2} + (3 sin A - 4 {sin}^{3} A)^{2}$
using formula
$\Rightarrow (- 1)^{2} ({cos}^{2} 3 A) + {sin}^{2} 3 A$
$\Rightarrow {cos}^{2} A + {sin}^{2} 3 A$
$= 1$
$cos 3 A = 4 {cos}^{3} A - 3 cos A$
$sin 3 A = 3 sin A - 4 {sin}^{3} A$
${cos}^{2} θ + {sin}^{2} θ = 1$

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