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SSC CHSL 2020 · Question 51 of 91

If cos θ = 4x 1+4x2 ​ , then what is the value of sin θ ? 1−4x2

Trigonometry

  1. A4x
  2. B1+4x2Correct
  3. C1−4x2
  4. D4x2

Answer: B. 1+4x2

Explanation

Given: cos θ = 4x 1+4x2 ​ Formula: sin 2θ + cos 2θ = 1 Calculation: sin 2θ = 1 - ( 1+4x 4x 2 2) ​ (1+4x2 )2 −16x2 ⇒ (1+4x2 )2 ​ 1+8x2 +16x4 −16x2 ⇒ (1+4x2 )2 ​ 2 4 ⇒ 1−8x +16x (1+4x2 )2 ​ 2 2 ⇒ (1−4x ) (1+4x2 )2 ​ 2 ∴ sin θ = 1−4x 1+4x2 ​

Source: SSC CHSL 2020 (Tier-I) Prev. Year Paper (04-Aug-2021) (Shift 1) — prepp.in solved paper · reliable-secondary

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