A) \[(\cos 25\theta +i\sin 25\theta )\]
B) \[i(\cos 25\theta +i\sin 25\theta )\]
C) \[i\,(\cos 25\theta -i\sin 25\theta )\]
D) \[(\cos 25\theta -i\sin 25\theta )\]
Correct Answer: D
Solution :
\[\sin \theta -i\cos \theta =-{{i}^{2}}\sin \theta -i\cos \theta =-i(\cos \theta +i\sin \theta )\] Given expression is \[{{(-i)}^{3}}[\cos (-10\theta -18\theta +3\theta )+i\sin (-25\theta )]\] = \[i\,(\cos 25\theta -i\sin 25\theta ]\].
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