We express \[\frac{{{(\cos 2\theta -i\sin 2\theta )}^{4}}{{(\cos 4\theta +i\sin 4\theta )}^{-5}}}{{{(\cos 3\theta +i\sin 3\theta )}^{-2}}{{(\cos 3\theta -i\sin 3\theta )}^{-9}}}\] in the form of \[x+iy\], we get [Karnataka CET 2001]

\[\cos 23\theta -i\,\sin 23\theta \]

\[\cos 49\theta -i\,\sin 49\theta \]

\[\cos 49\theta +i\,\sin 49\theta \]

\[\cos 21\theta +i\,\sin 21\theta \]

We express \[\frac{{{(\cos 2\theta -i\sin 2\theta )}^{4}}{{(\cos 4\the

1.	We express \[\frac{{{(\cos 2\theta -i\sin 2\theta )}^{4}}{{(\cos 4\theta +i\sin 4\theta )}^{-5}}}{{{(\cos 3\theta +i\sin 3\theta )}^{-2}}{{(\cos 3\theta -i\sin 3\theta )}^{-9}}}\] in the form of \[x+iy\], we get [Karnataka CET 2001]
A.	\[\cos 49\theta -i\,\sin 49\theta \]
B.	\[\cos 23\theta -i\,\sin 23\theta \]
C.	\[\cos 49\theta +i\,\sin 49\theta \]
D.	\[\cos 21\theta +i\,\sin 21\theta \]
Answer» B. \[\cos 23\theta -i\,\sin 23\theta \]

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We express \[\frac{{{(\cos 2\theta -i\sin 2\theta )}^{4}}{{(\cos 4\theta +i\sin 4\theta )}^{-5}}}{{{(\cos 3\theta +i\sin 3\theta )}^{-2}}{{(\cos 3\theta -i\sin 3\theta )}^{-9}}}\] in the form of \[x+iy\], we get [Karnataka CET 2001]

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