If cot θ + tan θ = 2{rm{cosec}}θ , general value of θ is

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Trigonometrical Equations

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If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is

A

$n\pi \pm \frac{\pi }{3}$

B

$n\pi \pm \frac{\pi }{6}$

C

$2n\pi \pm \frac{\pi }{3}$

D

$2n\pi \pm \frac{\pi }{6}$

Solution

(c) $\cot \theta + \tan \theta = 2{\rm{ cosec}}\theta $

==> $\frac{2}{{\sin \theta }} = \frac{1}{{\sin \theta \cos \theta }}$

$ \Rightarrow $ $\cos \theta = \frac{1}{2}$ or $\sin \theta = 0$

$ \Rightarrow $ $\theta = 2n\pi \pm \frac{\pi }{3}$ or $\theta = n\pi $.

Standard 11

Mathematics

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