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SSC CHSL 2024 PYQ — Question 62

SSC CHSL - 08 July 2024 - Shift 4 • Quantitative Aptitude • Q62

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If cos4θcos^4θ — sin4θsin^4θ = 4/5, then find the value of sin4θsin4θ.

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 242524\over25.

cos4 θ - sin4θ = 4/5

⇒ (cos2θ)2 - (sin2θ)2 = 4/5

⇒ (cos2θ + sin2θ)(cos2θ - sin2θ) = 4/5

⇒ 1 × (cos2θ - sin2θ) = 4/5

⇒ cos 2θ = 4/5

Now,

⇒ sin22θ + cos22θ = 1

⇒ sin22θ + (4/5)2 = 1

⇒ sin22θ + 16/25 = 1

⇒ sin22θ = 1 - 16/25

⇒ sin22θ = 9/25

⇒ sin2θ = 3/5

Now,

⇒ sin4θ = 2 sin 2θ cos2θ

⇒ sin 4θ = 2 × 3/5 × 4/5

⇒ sin 4θ = 24/25