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SSC CHSL 2020 PYQ — Question 73

SSC CHSL - 14th October 2020 - Shift 2 • Quantitative Aptitude • Q73

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If A and B are acute angles and SecA = 3; CotB = 4, then the value of  is:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e 322/323.

Understanding/Application

secA = 3 

cosA = 1/3

sinA = √(1 - cos2A) = √{1 - (1/9)} = √(8/9) = 2√2/3

cosecA = 3/2√2

cotA = cosA/sinA = (1/3)/(2√2/3) = 1/2V2

cotB = 4

tanB = 1/4

secB = √(1 + tan2B) = √(1 + 1/16) = √(17/16) = √17/4

cosB = 4/√17

sinB = √(1 - cos2B) = √(1 - 16/17) = 1/√17

(cosec2A + sin2B)/(cot2A + sec2B) 

= {(3/2√2)2 + (1/√17)2}/{(1/2√2)2 + (√17/4)2}

= (9/8 + 1/17)/(1/8 + 17/16)

= (161/136)/(152/128)

= 322/323