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SSC CGL 2021 PYQ — Question 55

SSC CGL - 17 Aug 2021 - Shift 3 • Quantitative Aptitude • Q55

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If 4 sin2 (2x - 10)° = 3, 0 ≤ (2x - 10) ≤ 90 then, find the value of sin4(x−5)∘+cos4(x−5)∘1−2sin2(3x−15)∘cos(3x−15)∘\frac{sin^4(x-5)^\circ +cos^4(x-5)^\circ}{1- 2sin^2(3x-15)^\circ cos(3x-15)^\circ}

 

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Correct answer: A

Explanation

The correct answer is Option 1 i.e ​​​​​​ 5/8.

⇒ 4 sin2 (2x - 10)° = 3

⇒ sin2 (2x - 10)° = 3/4

⇒ sin(2x - 10)° = 32\frac{\sqrt{3}}{2}

⇒ sin(2x - 10)° = sin 60°

⇒ (2x -10) = 60

⇒ 2x = 70

⇒ x = 35°.

⇒sin4(x−5)∘+cos4(x−5)∘1−2sin2(3x−15)∘cos(3x−15)∘\Rightarrow\frac{sin^4(x-5)^\circ +cos^4(x-5)^\circ}{1- 2sin^2(3x-15)^\circ cos(3x-15)^\circ}

 ⇒sin4(35−5)+cos4(35−5)1−2sin2(105−15)cos(105−15)⇒sin4(30)+cos2(30)1−2sin2(90)cos(90)\Rightarrow\frac{sin^4(35-5)+cos^4(35-5)}{1- 2sin^2(105-15)cos(105-15)} \\ \Rightarrow\frac{sin^4(30)+cos^2(30)}{1- 2sin^2(90)cos(90)}

⇒sin4(30)+cos4(30)\Rightarrow {sin^4(30)+cos^4(30)} = (12)4+(32)4(\frac12)^4 + (\frac{\sqrt3}{2})^4= 1/16 + 9/16

⇒ 10/16 = 5/8