A) \[\left] \frac{\pi }{4},\frac{\pi }{2} \right[\]
B) \[\left] \frac{5\pi }{8},\frac{3\pi }{4} \right[\]
C) \[\left] 0,\frac{\pi }{4} \right[\]
D) \[\left] \frac{\pi }{2},\frac{5\pi }{8} \right[\]
Correct Answer: A
Solution :
\[f(x)={{\sin }^{4}}{{x}_{3}}+{{\cos }^{4}}x\] \[f(x)=4{{\sin }^{3}}x+\cos x-4{{\cos }^{3}}x\sin x\] \[=4\sin x\cos x({{\sin }^{2}}-{{\cos }^{2}}x)\] \[=-2\sin 2x.\cos 2x\] \[=-\sin 4x>0\] \[\Rightarrow \pi <4x<2\pi \] \[\frac{\pi }{4}<x<\frac{\pi }{2}\]
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