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SSC CPO 2022 PYQ — Question 130

SSC CPO - 9 Nov 2022 - Shift 3 • Quantitative Aptitude • Q130

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Given that A and B are second-quadrant angles, sin⁡A=13\sin A = \frac{1}{3} and sin⁡B=15\sin B = \frac{1}{5}, then find the value of cos (A - B).

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 83+115\frac{8\sqrt{3}+1}{15}.

Given that

sin⁡A=13\sin A = \frac{1}{3} and sin⁡B=15\sin B = \frac{1}{5}, 

The value of cos (A - B)

⇒ cos (A - B) = cos A cos B + sin A sin B

As we know,

⇒ cos A = (1−sin2A) \sqrt(1 - sin^2A) =  (1−(1/32)) \sqrt(1 - (1/3^2)) = (8/9)\sqrt(8/9) = 222\sqrt2/3

⇒ cos B =  (1−sin2B) \sqrt(1 - sin^2B) = (1−(1/5)2) \sqrt(1 - (1/5)^2) = (24/25)\sqrt(24/25) = 26\sqrt6/5

Hence, the value of cos (A - B) = 222\sqrt2/3 ×  26\sqrt6/5 + (1/3)(1/5) = 83+115\frac{8\sqrt{3}+1}{15}