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SSC CPO 2024 PYQ — Question 132

SSC CPO - 29 June 2024 - Shift 3 • Quantitative Aptitude • Q132

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If cosA = 45\frac{4}{5}, then find value of ( 8 + sinA)(3 - tanA)

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Correct answer: B

Explanation

The correct answer is option 2 i.e.  38720\frac{387}{20}.

We know that sin²(A) + cos²(A) = 1.

Given cos(A) = 4/5, we can find sin(A):

sin²(A) + (4/5)² = 1 sin²(A) = 1 - 16/25 sin²(A) = 9/25 sin(A) = ±3/5

Since we're dealing with a right-angled triangle, sin(A) is positive. So, sin(A) = 3/5.

tan(A) = sin(A) / cos(A) = (3/5) / (4/5) = 3/4

(8 + sin(A))(3 - tan(A)) = (8 + 3/5)(3 - 3/4) = (43/5)(9/4) = 387/20