Question

Suppose $\cos A$ is given. If only one value of $\cos \left(\frac{A}{2}\right)$ is possible, then $A$ must be

• A. An odd multiple of ${90}^o$
• B. A multiple of ${90}^o$
• C. An odd multiple of ${180}^o$
• D. A multiple of ${180}^o$

Answer 1

The correct option is C An odd multiple of ${180}^o$

$2{\cos }^2\frac{A}{2}-1=\cos A$

$\Rightarrow 2{\cos }^2\frac{A}{2}=\cos A+1\Rightarrow \cos \frac{A}{2}=\pm \sqrt{\frac{1+\cos A}{2}}$

If one value of $A$ possible then $\cos A$ must be ${}^{\prime }-1^{\prime }$, therefore

${}^{\prime }{A}^{\prime }$ must be odd multiple ${180}^o$