Question

The most general value of $\theta$ which satisfies both the equations $\tan \theta =-1$ and $\cos \theta =\frac{1}{\sqrt{2}}$ is
Here $n$ is any integer.

• A. $n\pi +7\frac{\pi }{4}$
• B. $2n\pi +\frac{7\pi }{4}$
• C. $n\pi +(-1{)}^n\frac{7\pi }{4}$
• D. $\frac{7n\pi }{4}$

Answer 1

The correct option is B $2n\pi +\frac{7\pi }{4}$

$\tan \theta =-1$ and $\cos \theta =\frac{1}{\sqrt{2}}$

Common solutions lie in $4^{th}$ quadrant which is $\theta =\frac{7\pi }{4}$

Hence general solution is $\theta =2n\pi +\frac{7\pi }{4}$, where$n\in I$