CDS 2026 · PYQ · Trigonometric Identities · medium
p = sinθ/(1 + cosθ + sinθ) and q = (1 + sinθ)/(1 + sinθ − cosθ). What is (p + 1/q)(q + 1/p) equal to?
Answer
The correct answer is C: 9/2. Using 2pq = 1, so pq = 1/2. Expand (p + 1/q)(q + 1/p) = pq + p/p + q/q + 1/(pq) = pq + 1 + 1 + 1/pq = pq + 2 + 1/pq = 1/2 + 2 + 2 = 9/2.
- A.1/2
- B.17/4
- C.9/2✓ Correct
- D.21/4
Using 2pq = 1, so pq = 1/2. Expand (p + 1/q)(q + 1/p) = pq + p/p + q/q + 1/(pq) = pq + 1 + 1 + 1/pq = pq + 2 + 1/pq = 1/2 + 2 + 2 = 9/2.
💡
Practice unlimited CDS PYQs + AI-tracked progress on each topic.
Sign up free →More Trigonometric Identities 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