Sarkari RiseLogin
CDS 2023 · PYQ · Trigonometry · medium

If tan x = (sin θ + cos θ)/(sin θ − cos θ), π/4 < θ < π/2, then what is √2 sin x equal to?

Answer

The correct answer is A: sin θ + cos θ. tan x = (sinθ+cosθ)/(sinθ−cosθ). Then sin x = (sinθ+cosθ)/√((sinθ+cosθ)²+(sinθ−cosθ)²) = (sinθ+cosθ)/√2.

  1. A.sin θ + cos θ✓ Correct
  2. B.(sin θ + cos θ)/2
  3. C.sin θ − cos θ
  4. D.(sin θ − cos θ)/2

Explanation

tan x = (sinθ+cosθ)/(sinθ−cosθ). Then sin x = (sinθ+cosθ)/√((sinθ+cosθ)²+(sinθ−cosθ)²) = (sinθ+cosθ)/√2. So √2 sin x = sin θ + cos θ.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →

More Trigonometry questions

Want more CDS practice?

Free daily 10-Q quiz · adaptive mocks · 49,000+ practice questions (19,000+ verified PYQs) · AI doubt solver in Hindi + English

Sign up freeMore Trigonometry practice