If cos θ = - frac{1}{{√ 2 }} and tan θ = 1 , then general value of θ is

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Trigonometrical Equations

easy

If $\cos \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1$, then the general value of $\theta $ is

A

$2n\pi + \frac{\pi }{4}$

B

$(2n + 1)\,\pi + \frac{\pi }{4}$

C

$n\pi + \frac{\pi }{4}$

D

$n\pi \pm \frac{\pi }{4}$

Solution

(b) $\cos \theta = – \frac{1}{{\sqrt 2 }} \Rightarrow \theta = \frac{{3\pi }}{4},\,\frac{{5\pi }}{4}$;

$\tan \theta = 1 \Rightarrow \theta = \frac{\pi }{4},\,\frac{{5\pi }}{4}$

$\therefore $ The general value is $2n\pi + \frac{{5\pi }}{4}$ or $(2n + 1)\pi + \frac{\pi }{4}$.

Standard 11

Mathematics

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