46. Find the minimum and maximum values of the function $\varphi(x)=\sin ^{6} x+\cos ^{6} x$.
46. $\varphi(x)=\frac{1+3 \cos ^{2} 2 x}{4}$. The maximum value of $\varphi(x)$ is 1, and the minimum value is $\frac{1}{4}$.

![](https://cdn.mathpix.com/cropped/2024_05_21_ec9ddf54a7c86775293eg-120.jpg?height=483&width=371&top_left_y=267&top_left_x=1322)

Fig. 29