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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
General solution of the equation $\cot \theta-\tan \theta=2$ is
  • A
    $\theta=n \pi+\frac{\pi}{4}$
  • ✓
    $\theta=\frac{ n \pi}{2}+\frac{\pi}{8}$
  • C
    $\theta=\frac{ n \pi}{2} \pm \frac{\pi}{8}$
  • D
    $\theta=n \pi \pm \frac{\pi}{4}$
✓

Answer

Correct option: B.
$\theta=\frac{ n \pi}{2}+\frac{\pi}{8}$
(B) $\cot \theta-\tan \theta=2 \Rightarrow \frac{\cos \theta}{\sin \theta}-\frac{\sin \theta}{\cos \theta}=2$
$\begin{array}{l}\therefore \cos ^2 \theta-\sin ^2 \theta=\sin 2 \theta \Rightarrow \cos 2 \theta=\sin 2 \theta \\ \therefore \tan 2 \theta=\tan \frac{\pi}{4} \Rightarrow 2 \theta=n \pi+\frac{\pi}{4} \\ \therefore \quad \theta=\frac{n \pi}{2}+\frac{\pi}{8}\end{array}$

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