A) \[\pi ,\pi ,\pi \]
B) \[\pi ,\,\,2\pi ,\,\,\pi \]
C) \[\pi ,\,\,\pi ,\,\,\frac{\pi }{2}\]
D) \[\pi ,\,\,\frac{\pi }{2},\pi \]
Correct Answer: C
Solution :
| \[f(x+\pi )={{(-1)}^{\left[ \frac{2x}{\pi }+2 \right]}}={{(-1)}^{\frac{2x}{\pi }}}=f(x)\] |
| period \[=\pi \] |
| \[g\,\,(x+\pi )=g(x)\to period\,\,=\pi \] |
| \[\phi \,(x)=f(x)\,\,g(x)={{(-\,1)}^{\left[ \frac{2x}{\pi } \right]}}.(|\,sinx\,|-|\,\cos x\,|)\] |
| \[\phi \,\,\left( \frac{\pi }{2}+x \right)={{(-\,1)}^{\left[ \frac{2x}{\pi } \right]}}.(-\,1)[|\,\cos x\,|-|\,\cos x\,|]\] |
| \[=f(x).\,g(x)\to period=\frac{\pi }{2}\] |
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