The most general value of $\theta$ which satisfies both the equations $\tan 8=-1$ and $\cos…

The most general value of $\theta$ which satisfies both the equations $\tan 8=-1$ and $\cos \theta=\frac{1}{\sqrt{2}}$ is
  1. $n \pi+\frac{7 \pi}{4}$
  2. $2 n \pi+\frac{7 \pi}{4}$
  3. $n \pi+(-1)^n \frac{7 \pi}{4}$
  4. $\frac{7 n \pi}{4}$

Solution

Given trigonometric equations are $\tan \theta=-1$ and $\cos \theta=\frac{1}{\sqrt{2}}$ $\begin{array}{ll}\Rightarrow & \sin \theta=-1 / \sqrt{2} \\ \Rightarrow & \sin \theta=\sin \frac{7 \pi}{4} \\ \therefore & \theta=2 n \pi+\frac{7 \pi}{4}\end{array}$

Asked in: AP EAMCET 2011

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