Question

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

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is C

We have $\tan \theta =-1$ and $\cos \theta =\frac{1}{\sqrt{2}}$
The value of $\theta$ lying between $\frac{3\pi }{2}$ and $2\pi$ and satisfying these two is $\frac{7\pi }{4}$. Therefore the most general
solution is $\theta =2n\pi +7\pi /4$ where $n\in Z$