A) \[g(x)+g(\pi )\]
B) \[g(x)-g(\pi )\]
C) \[g(x)g(\pi )\]
D) \[g(x)/g(\pi )\]
Correct Answer: A
Solution :
\[g(x+\pi )=\int_{0}^{x+\pi }{{{\cos }^{4}}t\,dt=\int_{0}^{\pi }{{{\cos }^{4}}t\,dt+\int_{\pi }^{x+\pi }{{{\cos }^{4}}t\,dt}}}\] \[=g(\pi )+f(x)\] \[f(x)=\int_{0}^{x}{{{\cos }^{4}}u\,du=g(x)}\], \[(\because t=\pi +u)\] \[\therefore \,\,g(x+\pi )=g(x)+g(\pi )\].
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