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SSC CHSL Model Paper 4

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Question : 68 of 100

Marks: +1, -0

If 8 sin x = 4 + cos x, the values of sin x are

$\frac{3}{5}, \frac{5}{13}$
$\frac{3}{13}, \frac{5}{13}$
$\frac{3}{5}, \frac{5}{3}$
$\frac{3}{13}, \frac{5}{3}$

Solution:

8 sin x = 4 + cos x

8 sin x – 4 = cos x

Squaring both the sides, we get:

64 sin

^{2}

x + 16 – 64 sin x = cos

^{2}

x

⇒ 64 sin

^{2}

x + 16 – 64 sin x = 1 – sin

^{2}

x

⇒ 65 sin

^{2}

x – 64 sin x + 15 = 0

⇒ 65 sin

^{2}

x – 39 sin x – 25 sin x + 15 = 0

⇒ 13 sin x (5 sin x – 3) – 5(5 sin x – 3) = 0

⇒ (5 sin x – 3) (13 sin x – 5) = 0

⇒ sin x =

\frac{3}{5}, \frac{5}{13}

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