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SSC CGL 2021 PYQ — Question 66

SSC CGL - 24 Aug 2021 - Shift 3 • Quantitative Aptitude • Q66

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In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
John was an artist (1)______ profession. He was very (2)______ at his work and could
(3)______ any subject he could think of, but circumstances forced him to (4)______ in
(5)______ the work of renowned artists.

simplify : ,0° < θ < 90°

Show answer & explanation

Correct answer: B

Explanation

 The correct answer is option 2 i.e. 1

(Sinθ + secθ)2 + (Cosθ + Cosecθ)2/(1 + secθcosecθ)2

1/Sinθ = Cosecθ

1/Cosθ = Secθ

Sin2θ + Cos2θ = 1

(A + B)2 = A2 + 2AB + B2

(Sinθ + secθ)2 + (Cosθ + Cosecθ)2

= (Sinθ + 1/Cosθ)2 + (Cosθ + 1/Sinθ)2

= Sin2θ + 2 × Sinθ × (1/Cosθ) + 1/Cos2θ + Cos2​θ + 2 × Cosθ × (1/Sinθ) + 1/Sin2θ

= (Sin2θ + Cos2​θ) + {(2Sinθ/Cosθ) + (2Cosθ Sinθ)} + (1/Cos2θ + 1/Sin2θ)

= 1 + {2/(Cosθ × Sinθ)} + {1/(Cos2θ × Sin2θ)}

= (1 + 2 × Secθ × Cosecθ + Sec2θ × Cosec2θ)

= (1 + SecθCosecθ)2

(Sinθ + secθ)2 + (Cosθ + Cosecθ)2/(1 + secθcosecθ)2

= (1 + SecθCosecθ)2/(1 + SecθCosecθ)2

= 1