$\mathop {\underline {1 + {{\sin }^4}x} }\limits_{ \ge 1} = \mathop {\underline {{{\cos }^2}3x} }\limits_{ \le 1}$ Now for equality to hold sin 4 x = 0 & cos 2 3x = 1 sin 4 = 0 $\Rightarrow$ x = -2$\pi$, - $\pi$, 0, $\pi$, 2$\pi$ All of which satisfy cos 2 3x = 1 $\Rightarrow$ 5 solutions