A) \[\cos \theta -i\sin \theta \]
B) \[\cos 9\theta -i\sin 9\theta \]
C) \[\sin \theta -i\cos \theta \]
D) \[\sin 9\theta -i\cos 9\theta \]
Correct Answer: D
Solution :
\[\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{(\sin \theta +i\cos \theta )}^{5}}}=\frac{{{(\cos +i\sin \theta )}^{4}}}{{{i}^{5}}{{\left( \frac{1}{i}\sin \theta +\cos \theta \right)}^{5}}}\] \[=\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{i\,{{(\cos \theta -i\sin \theta )}^{5}}}=\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{i\,{{(\cos \theta +i\sin \theta )}^{-5}}}\] (By property) \[=\frac{1}{i}{{(\cos \theta +i\sin \theta )}^{9}}=\sin 9\theta -i\cos 9\theta \].
You need to login to perform this action.
You will be redirected in
3 sec
