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SSC CPO 2023 PYQ — Question 138

SSC CPO - 05 Oct 2023 - Shift 2 • Quantitative Aptitude • Q138

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Find the value of sin239o+sin2(90o−39o)cos235o+cos2(90o−35o)+3tan15otan75o\frac{sin^2 39^o+sin^2 (90^o-39^o)}{cos^2 35^o+cos^2(90^o-35^o)}+3tan15^otan75^o:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 4.

Given that

The value of sin239o+sin2(90o−39o)cos235o+cos2(90o−35o)+3tan15otan75o\frac{sin^2 39^o+sin^2 (90^o-39^o)}{cos^2 35^o+cos^2(90^o-35^o)}+3tan15^otan75^o

⇒ sin239o+sin2(90o−39o)cos235o+cos2(90o−35o)+3tan15otan75o\frac{sin^2 39^o+sin^2 (90^o-39^o)}{cos^2 35^o+cos^2(90^o-35^o)}+3tan15^otan75^o

⇒ sin239o+cos239ocos235o+sin235o+3tan15otan(90o−15o)\frac{sin^2 39^o+cos^2 39^o}{cos^2 35^o+sin^235^o}+3tan15^otan(90^o - 15^o)

⇒ 1+3tan15ocot15o1+3tan15^ocot15^o

⇒ 1 + 3

⇒ 4