UPSC One
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2018 · Q62

If sin A + cos A = p and sin³A + cos³A = q, then which one of the following is correct?

Elementary MathematicsTrigonometry
  1. Ap³ - 3p + q = 0
  2. Bq³ - 3q + 2p = 0
  3. Cp³ - 3p + 2q = 0
  4. Dp³ + 3p + 2q = 0

Explanation

Write q = (sinA + cosA)(sin²A − sinAcosA + cos²A) = p(1 − sinAcosA). With sinAcosA = (p² − 1)/2 this gives q = p(3 − p²)/2, i.e. p³ − 3p + 2q = 0, option (C).