SarkariPYQ

SSC CPO 2022 PYQ — Question 139

SSC CPO - 11 Nov 2022 - Shift 3 • Quantitative Aptitude • Q139

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The value of sin  Acot  A+cosec  −sin  Acot  A−cosec  +1 {{sin\;A} \over cot\;A+cosec\;}- {{sin\;A} \over cot\;A-cosec\;}+1 is :

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 3

Given that

 The value of sin  Acot  A+cosec  A−sin  Acot  A−cosec  A+1 {{sin\;A} \over cot\;A+cosec\;A}- {{sin\;A} \over cot\;A-cosec\;A}+1

⇒ sin  A(cot  A−cosec  A)−sin  A(cot  A+cosec  A)cot2  A−cosec2  A+1 {{sin\;A(cot\;A-cosec\;A)-sin\;A(cot\;A+cosec\;A)} \over cot^2\;A-cosec^2\;A}+1

⇒ sin  Acot  A−1−sin  Acot  A−1)cot2  A−cosec2  A+1 {{sin\;Acot\;A-1-sin\;Acot\;A-1)} \over cot^2\;A-cosec^2\;A}+1

⇒ −2−1+1 {{-2} \over -1}+1

⇒ 2 + 1

⇒ 3