$3 sin x + 4 cos x = 5$ , then $4 sin x - 3 cos x =$

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Solution

The correct option is A $0$
$3 sin x + 4 cos x = 5$

$⟹ 9 {sin}^{2} x = (5 - 4 {cos}^{2} x)^{2}$

$⟹ 25 {cos}^{2} x - 40 cos x + 16 = 0$

$cos x = \frac{40 \pm \sqrt{40^{2} - 4 (25) (16)}}{2 \times 25}$

$⟹ cos x = \frac{4}{5}$

${sin}^{2} x = 1 - (\frac{4}{5})^{2} ⟹ sin x = \frac{3}{5}$

$4 sin x - 3 cos x = 4 (\frac{4}{5}) - 3 (\frac{3}{5}) = 0$

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A = \dots \dots \dots, B = \dots \dots \dots .

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