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SSC CGL 2022 PYQ — Question 73

SSC CGL - 18 April 2022 - Shift 3 • Quantitative Aptitude • Q73

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If A = 10°, what is the value of:12sin3A+5cos(5A−5o)9sin9A2−4cos(5A+10o)\frac{12 sin 3A + 5cos(5A - 5^o)}{9sin\frac{9A}{2}- 4cos(5A + 10^o)}

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  62+59−22\frac{6\sqrt2+5}{9-2\sqrt2}

Calculations:

Let us take value of A be 10°

⇒ 12sin30+5cos(50−5)9sin45−4cos(50+10)\dfrac{12 sin 30 + 5cos(50 - 5)}{9sin45- 4cos(50 + 10)}

⇒ 12sin30+5cos459sin45−4cos60\dfrac{12sin30 + 5cos45}{9sin45 - 4cos60}

⇒ 12×1/2+5×1/29/2−4×1/2\dfrac{12 \times 1/2 + 5 \times 1/\sqrt2}{9/\sqrt2- 4 \times 1/2}

⇒ 6+5/29/2−2\dfrac{6 + 5/\sqrt2}{9/\sqrt2 - 2}

⇒ 62+59−22\dfrac{6\sqrt2 + 5}{9 - 2\sqrt2}