Question

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

A
An odd multiple of 90o
B
A multiple of 90o
C
An odd multiple of 180o
D
A multiple of 180o

Solution

## The correct option is C An odd multiple of $${ 180 }^{ o }$$$$2\cos^{2} \dfrac {A}{2} - 1 = \cos A$$$$\Rightarrow 2\cos^{2} \dfrac {A}{2} = \cos A + 1\Rightarrow \cos \dfrac {A}{2} = \pm \sqrt {\dfrac {1 + \cos A}{2}}$$If one value of $$A$$ possible then $$\cos A$$ must be $$'-1'$$, therefore$$'A'$$ must be odd multiple $$180^o$$Mathematics

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