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SSC CGL 2022 PYQ — Question 59

SSC CGL - 11 April 2022 - Shift 3 • Quantitative Aptitude • Q59

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If sec A = 178\frac{17}{8} , given thatA < 90°, what is the value of the following ? 34sinA+15cotA68cosA−16tanA\frac{34sinA+15cotA}{68cosA - 16 tanA}

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 19

Concept used = sec A = (hypotenuse/base)

Solution :

Given sec A = 17/8                        

Let Hypotenuse be 17 x and base be 8x,

then, Perpendicular = 15x

Therefore, sinA = 15/17 ; cosA = 8/17 ; cotA = 8/15 ; tanA = 15/8

Applying the values in required equation,

34sinA+15cotA68cosA−16tanA\frac{34sinA+15cotA}{68cosA - 16 tanA} = (34×15/17)+(15×8/15)(68×8/17)−(16×15/8)(34 × 15/17) + (15 × 8/15)\over(68 × 8/17) - (16 × 15/8) = (30 + 8)/(32 - 30) = 38/2 = 19.