# How can one find the root of sesquilinear form with positive definite matrix?

How can one find the root of sesquilinear form with positive definite matrix?
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reinmelk3iu
$2{\mathrm{sin}}^{2}\left(x\right)=\underset{=1}{\underset{⏟}{{\mathrm{cos}}^{2}\left(2x\right)+{\mathrm{sin}}^{2}\left(2x\right)}}$
Whence
${\mathrm{sin}}^{2}\left(x\right)=\frac{1}{2}$
Can you proceed from here?
Solution
$\mathrm{sin}\left(x\right)=±\frac{\sqrt{2}}{2}$
This is a well known value and it's $\pi /4$ radians and $3\pi /4$ radians. Since we have ${\mathrm{sin}}^{2}$, to be then explicit in the solution we have also $-\pi /4$ and $5\pi /4$ radians: