Given: sinx = \(\frac{\sqrt{5}}{3}\)
To find: cos2x
We know that,
cos2x = 1 – 2sin2x
Putting the value, we get
cos2x = 1 - 2\((\frac{\sqrt{5}}{3})^{2}\)
cos2x = 1 - 2 x \(\frac{5}{9}\)
cos2x = 1 - \(\frac{10}{9}\)
cos2x = \(\frac{9\,-\,10}{9}\)
∴ cos2x = -\(\frac{1}{9}\)
