Question

Construct the graphs of the following functions and carry out a complete investigation .
y = $si{n}^{4}x+co{s}^{4}x$

Answer 1

$y={\sin }^{4}x+{\cos }^{4}x$

$={({\sin }^{2}x+{\cos }^{2}x)}^2-2{\sin }^{2}x{\cos }^{2}x$

$=1-\frac{1}{2}{\sin }^{2}2x$

We know that the period of $\sin x$ is $2\pi$ so, the period of $\sin 2x$ is $\pi$

Hence, it is clear that the period of ${\sin }^2\left(2x\right)$ is $\frac{\pi }{2}$

So, the period of the given function will be $\frac{\pi }{2}$