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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?

  1. A.1/2
  2. B.17/4
  3. C.9/2✓ Correct
  4. D.21/4

Explanation

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.
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