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SMO 2013 Senior Round 1 Question 6

SMO · SMO 2013 Senior Round 1

Question 6

If $0\lt \theta\lt \pi/4$ is such that $\operatorname{cosec}\theta-\sec\theta=\sqrt{13}/6$, then $\cot\theta-\tan\theta$ equals
  1. $\frac{\sqrt{13}}6$
  2. $\frac{\sqrt{12}}6$
  3. $\frac{\sqrt5}6$
  4. $\frac{13}6$
  5. $\frac56$