Question:
If $\sin \mathrm{x}=\frac{\sqrt{5}}{3}$ and $0<\mathrm{x}<\frac{\pi}{2}$ find the values of $\cos 2 x$
Solution:
Given: $\sin \mathrm{x}=\frac{\sqrt{5}}{3}$
To find: $\cos 2 x$
We know that
$\cos 2 x=1-2 \sin ^{2} x$
Putting the value, we get
$\cos 2 x=1-2\left(\frac{\sqrt{5}}{3}\right)^{2}$
$\cos 2 x=1-2 \times \frac{5}{9}$
$\cos 2 x=1-\frac{10}{9}$
$\cos 2 x=\frac{9-10}{9}$
$\therefore \cos 2 x=-\frac{1}{9}$
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