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SSC CGL 2022 PYQ — Question 61

SSC CGL - 03 Dec 2022 - Shift 1 • Quantitative Aptitude • Q61

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11+cos(90°−θ)+11−cos(90°−θ)={{1} \over 1+cos(90°-\theta)}+{{1} \over 1-cos(90°-\theta)}= ___________.

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 2sec2 θ.

Formula used:

a2 - b2 = (a + b)(a - b)

1 - sin2θ = cos2θ

Calculations:

1/(1 + cos(90 - θ)) + 1/(1 - cos(90 - θ))

which can be written as

⇒ 1/(1 + sinθ) + 1/(1 - sinθ)

⇒ [1 - sinθ + 1 + sinθ]/(1 - sin2θ)

⇒ 2/cos2θ

⇒ 2sec2θ