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JAMB 2016 · UTME · Q10

Differentiate (cos⁡q−sin⁡q)2(\cos q - \sin q)^2 with respect to qq.

Worked solution (try it first)
  1. Expand: (cos⁡q−sin⁡q)2=cos⁡2q+sin⁡2q−2sin⁡qcos⁡q(\cos q - \sin q)^2 = \cos^2q + \sin^2q - 2\sin q\cos q.
  2. Use cos⁡2q+sin⁡2q=1\cos^2q + \sin^2q = 1 and 2sin⁡qcos⁡q=sin⁡2q2\sin q\cos q = \sin2q: the expression is 1−sin⁡2q1 - \sin2q.
  3. Differentiate: the 1 gives 0 and sin⁡2q\sin2q gives 2cos⁡2q2\cos2q.
  4. So the derivative is −2cos⁡2q-2\cos2q, option A.

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