IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 23

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Trigonometric Identities, with the answer and a step-by-step solution.

Trigonometric IdentitiesTrigonometryMultiple choiceMedium
If sin\theta + cos\theta = \frac{1}{2}, what is the value of cos4\theta?
  1. A
    \frac{1}{8}
  2. B
    -\frac{7}{8}
  3. C
    \frac{7}{8}
  4. D
    -\frac{1}{8}
Pick an option, then check.
Answer & solution

Answer: Option D

Square both sides: (sin θ + cos θ)² = 1/4.

The left side expands to sin²θ + cos²θ + 2 sin θ cos θ = 1 + sin 2θ.

So 1 + sin 2θ = 1/4, giving sin 2θ = −3/4.

Now use cos 4θ = 1 − 2 sin²2θ.

sin²2θ = 9/16, so cos 4θ = 1 − 2(9/16) = 1 − 9/8.

cos 4θ = −1/8.

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