Trigonometric Identities Question 305
Question: $ {{(\cos \alpha +\cos \beta )}^{2}}+{{(\sin \alpha +\sin \beta )}^{2}}= $
Options:
A) $ 4{{\cos }^{2}}\frac{\alpha -\beta }{2} $
B) $ 4{{\sin }^{2}}\frac{\alpha -\beta }{2} $
C) $ 4{{\cos }^{2}}\frac{\alpha +\beta }{2} $
D) $ 4{{\sin }^{2}}\frac{\alpha +\beta }{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{(\cos \alpha +\cos \beta )}^{2}}+{{(\sin \alpha +\sin \beta )}^{2}} $ $ ={{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +2\cos \alpha \cos \beta +{{\sin }^{2}}\alpha + $ $ {{\sin }^{2}}\beta +2\sin \alpha \sin \beta $ $ =2{1+\cos (\alpha -\beta )}=4{{\cos }^{2}}( \frac{\alpha -\beta }{2} ) $ .
BETA
