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JAMB 2011 · UTME · Q34

In a right-angled triangle, if tan⁡θ=34\tan\theta = \frac34, what is cos⁡θ−sin⁡θ\cos\theta - \sin\theta?

Worked solution (try it first)
  1. tan⁡θ=oppositeadjacent\tan\theta = \frac{\text{opposite}}{\text{adjacent}}
    =34= \frac34.
  2. Pythagoras gives the hypotenuse 9+16=5\sqrt{9 + 16} = 5.
  3. So cos⁡θ=45\cos\theta = \frac45 and sin⁡θ=35\sin\theta = \frac35.
  4. Then cos⁡θ−sin⁡θ=45−35\cos\theta - \sin\theta = \frac45 - \frac35
    =15= \frac15, option C.

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