A) 1
B) 0
C) \[\sin x\]
D) None
Correct Answer: A
Solution :
[a] We have \[f(x)=si{{n}^{2}}x+{{\sin }^{2}}(x+\pi /3)+\cos x\cos (x+\pi /3)\] \[=\frac{1-\cos 2x}{2}+\frac{1-\cos (2x+2\pi /3)}{2}+\] \[\frac{1}{2}\{2cos\,\,x\,cos(x+\pi /3)\}\] \[=\frac{1}{2}\left[ \frac{5}{2}-\left\{ \cos 2x+\cos \left( 2x+\frac{2\pi }{3} \right) \right\}+\cos \left( 2x+\frac{\pi }{3} \right) \right]\]\[=\frac{1}{2}\left[ \frac{5}{2}-2\cos \left( 2x+\frac{\pi }{3} \right)\cos \frac{\pi }{3}+\cos \left( 2x+\frac{\pi }{3} \right) \right]\] \[=\frac{5}{4}\]For all x. \[gof(x)=g(f(x))=g\left( \frac{5}{4} \right)=1\] \[[\because g\left( \frac{5}{4} \right)=1\] (Given)] Hence, \[gof(x)=1,\]for all x.
You need to login to perform this action.
You will be redirected in
3 sec
