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  9. Q59

SSC CHSL 2022 · Question 59 of 92

If (2 cos3 A - cos A) = (sin A - 2 sin3 A), then what is the value of A?

Trigonometry

  1. A90 °
  2. B30 °
  3. C45 °Correct
  4. D60 °

Answer: C. 45 °

Explanation

Given: (2 cos3 A - cos A) = (sin A - 2 sin3 A) Calculation: (2 cos3 A - cos A) = (sin A - 2 sin3 A) ⇒ (2 cos3 A + 2 sin3 A) = (sin A + cos A) ⇒ 2(cos A + sin A)(cos2 A + sin2 A - sin A.cos A) = (cos A + sin A) ⇒ 2(1 - sin A.cos A) = 1 ⇒ 2sin A.cos A = 1 ⇒ sin 2A = 1 = sin 90° ⇒ 2A = 90° ⇒ A = 45° Hence, the value of A is 45°.

Source: SSC CHSL 2022 (Tier-I) Previous Year Paper (21-Mar-2023) (Shift 2) — prepp.in solved paper · reliable-secondary

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