A) \[[-1,\,1]\]
B) \[(-1,\,0]\]
C) \[[0,\,1)\]
D) \[(-1,\,1)\]
Correct Answer: D
Solution :
\[a=\operatorname{Im}.\left( \frac{1+{{e}^{i2\theta }}}{2i{{e}^{i\theta }}} \right)=\operatorname{Im}.\left( \frac{{{e}^{-i\theta }}+{{e}^{i\theta }}}{2i} \right)\] \[=\operatorname{Im}.\left( \frac{2\cos \theta }{2i} \right)=-\cos \theta \] As\[z\ne \pm 1,\,\,\text{so}\,\,a\in (-1,\,\,1)\]You need to login to perform this action.
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