Most general value of θ satisfying equations tan θ = - 1 and cos θ = frac{1}{{√ 2 }} is

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Trigonometrical Equations

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The most general value of $\theta $ satisfying the equations $\tan \theta = - 1$ and $\cos \theta = \frac{1}{{\sqrt 2 }}$ is

A

$n\pi + \frac{{7\pi }}{4}$

B

$n\pi + {( - 1)^n}\frac{{7\pi }}{4}$

C

$2n\pi + \frac{{7\pi }}{4}$

D

None of these

Solution

(c) $\tan \theta = – 1 = \tan \left( {2\pi – \frac{\pi }{4}} \right) ,$

$\cos \theta = \frac{1}{{\sqrt 2 }} = \cos \left( {2\pi – \frac{\pi }{4}} \right)$

Hence general value is $2n\pi + \left( {2\pi – \frac{\pi }{4}} \right) = 2n\pi + \frac{{7\pi }}{4}$.

Standard 11

Mathematics

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