A) 0
B) 1
C) \[\sin {{1}^{o}}\]
D) None of these
Correct Answer: B
Solution :
\[+\cos x\cos \left( x+\frac{\pi }{3} \right)\] \[={{\sin }^{2}}x+{{\left( \sin x\cos \frac{\pi }{3}+\cos x\sin \frac{\pi }{3} \right)}^{2}}\] \[+\cos x\left( \cos x\cos \frac{\pi }{3}-\sin x\sin \frac{\pi }{3} \right)\] \[={{\sin }^{2}}x+\frac{{{\sin }^{2}}x}{4}+\frac{3{{\cos }^{2}}x}{4}+\frac{2\sqrt{3}}{2\cdot 2}\sin x\cos x\] \[+\frac{{{\cos }^{2}}x}{2}-\cos x\sin x\frac{\sqrt{3}}{2}\] \[={{\sin }^{2}}x+\frac{{{\sin }^{2}}x}{4}+\frac{3{{\cos }^{2}}x}{4}+\frac{{{\cos }^{2}}x}{2}\] \[=\frac{5{{\sin }^{2}}x}{4}+\frac{3{{\cos }^{2}}x+2{{\cos }^{2}}x}{4}\] \[=\frac{5}{4}({{\sin }^{2}}x+{{\cos }^{2}}x)=\frac{5}{4}\] \[\therefore \]\[gof(x)=g[f(x)]=g\left( \frac{5}{4} \right)=1\]
You need to login to perform this action.
You will be redirected in
3 sec
