[STEP][剑桥数学入学考试][01-S1-Q4][Trigonometry][De Moivre's Theorem][FP1] STEP

casperyc的马甲 2月前 240

  1. Show that $ \displaystyle \tan 3\theta = \frac{3\tan\theta -\tan^3\theta}{1-3\tan^2\theta} $ .
  2. Given that $\theta = \cos^{-1} (2/\sqrt5)$ and $0<\theta<\pi/2$, show that $ \tan 3\theta = 11/2\;. $
  3. Hence, or otherwise, find all solutions of the equations $ \displaystyle \tan(3\cos^{-1} x) = 11/2 $ ,
  4. $\displaystyle \cos ({\textstyle\frac13}\tan^{-1} y) = 2/\sqrt5$ .
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