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WAEC 2019 · Paper 1 · Q36

If tan⁡x=34\tan x = \frac34, 0∘<x<90∘0^\circ < x < 90^\circ, evaluate cos⁡x2sin⁡x\dfrac{\cos x}{2\sin x}.

Worked solution (try it first)
  1. cos⁡xsin⁡x=1tan⁡x\dfrac{\cos x}{\sin x} = \dfrac{1}{\tan x}, so cos⁡x2sin⁡x=12tan⁡x\dfrac{\cos x}{2\sin x} = \dfrac{1}{2\tan x}.
  2. Put in tan⁡x=34\tan x = \frac34: 12×34=13/2\dfrac{1}{2 \times \frac34} = \dfrac{1}{3/2}
    =23= \dfrac23, option D.

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