A) \[\cos (m\theta +n\varphi )\]
B) \[\cos (m\theta +n\varphi )\]
C) \[2\cos (m\theta +n\varphi )\]
D) \[2\cos (m\theta -n\varphi )\]
Correct Answer: C
Solution :
\[x=\cos \theta +i\sin \theta ={{e}^{i\theta }},y=\cos \varphi +i\sin \varphi ={{e}^{i\varphi }}\] \[\therefore \,\,\,\,\,{{x}^{m}}{{y}^{n}}+{{x}^{-m}}{{y}^{-n}}={{e}^{im\theta }}{{e}^{in\varphi }}+{{e}^{-im\theta }}{{e}^{-in\varphi }}\] \[={{e}^{i(m\theta +n\varphi )}}+{{e}^{-i\,\,(m\theta \,+n\varphi )}}\]\[=\cos (m\theta +n\varphi )+i\sin (m\theta +n\varphi )\] \[=2\cos (m\theta +n\varphi )\]You need to login to perform this action.
You will be redirected in
3 sec