Question

If sinx = √5/3 and 0 < x < π/2, find the values of tan 2x

Answer 1

To find: tan2x

From part (i) and (ii), we have

sin2x = \(\frac{4\sqrt{5}}{9}\)

And 2x = -\(\frac{1}{9}\)

We know that,

tanx = \(\frac{sinx}{cosx}\)

Replacing x by 2x, we get

tan2x = \(\frac{sin2x}{cos2x}\)

Putting the values of sin 2x and cos 2x, we get

∴ tan2x = -4√5