Consider \( f, g \) and \( h \) be three real valued function defined on \( R \). Let \( f(x)=\s...

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Consider \( f, g \) and \( h \) be three real valued function defined on \( R \).
Let \( f(x)=\sin 3 x+\cos x, g(x)=\cos 3 x+\sin x \) and \( h(x)=f^{2}(x)+g^{2}(x) \)
The length of a longest interval in which the function \( g=h(x) \) is increasing, is
(a) \( \pi / 8 \)
(b) \( \pi / 4 \)
(c) \( \pi / 6 \)
(d) \( \pi / 2 \)
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