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SSC CPO 2023 PYQ — Question 140

SSC CPO - 05 Oct 2023 - Shift 1 • Quantitative Aptitude • Q140

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If sin⁡  β=13,(sec  β−tan⁡  β)\sin\; \beta={{1} \over 3}, (sec\;\beta - \tan\;\beta)2 is equal to:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 1/2.

Given that

⇒  sin⁡  β=13,(sec  β−tan⁡  β)\sin\; \beta={{1} \over 3}, (sec\;\beta - \tan\;\beta)2

⇒ sin⁡β=13\sin\beta={{1} \over 3} = P/H

B = √(9 - 1) = √8 = 2√2

⇒ sec  βsec\;\beta = H/B = 3/2√2, tan⁡  β\tan\;\beta = P/B = 1/2√2

⇒ (sec  β−tan⁡  β)2(sec\;\beta - \tan\;\beta)^2 = ( 3/2√2 -  1/2√2)2 

⇒ (2/2√2)2

⇒ 1/2