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Find the most general value of $\theta$ satisfying the equation $\tan\theta=-1$ and $\cos \theta=\large\frac{1}{\sqrt 2}$

$\begin{array}{1 1}(A)\;n\pi+\large\frac{9\pi}{4}&(B)\;2n\pi+\large\frac{7\pi}{4}\\(C)\;3n\pi+\large\frac{7\pi}{4}&(D)\;2n\pi+\large\frac{9\pi}{5}\end{array} $

1 Answer

$\tan \theta=-1=\tan\large\frac{3\pi}{4}$$=\tan\large\frac{7\pi}{4}$
$\cos\theta=\large\frac{1}{\sqrt 2}$
$\cos\large\frac{\pi}{4}=\large\frac{1}{\sqrt 2}$
$\cos(2\pi-\large\frac{\pi}{4})=\large\frac{1}{\sqrt 2}=$$\cos\large\frac{7\pi}{4}$
Principal value for both $\tan\theta$ and $\cos\theta$ is $\large\frac{7\pi}{4}$
$\therefore$ general value is $2n\pi+\large\frac{7\pi}{4}$
Hence (B) is the correct answer.
answered Apr 18, 2014 by sreemathi.v
Why we add 2npi and not npi or other ?
General value of cos theta is 2npi +/- alpha
General value of tan theta is npi + alpha
Then by which formula we obtained the
General value of theta in this question

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