show that if $\beta$ is an acute angle and that $\tan\beta=2\sqrt2$ then $\cos\beta=\frac{1}{3}$

Question

show that if $\beta$ is an acute angle and that $\tan\beta=2\sqrt2$ then $\cos\beta=\frac{1}{3}$

This question question has stumped me as I see no obvious way to go with it. This is all I've done so far.

$$\tan\beta=2\sqrt2$$ $$\frac{\sin\beta}{\cos\beta}=2\sqrt2$$

Answer 1

Remember that

$$1+\tan^2\beta=\frac1{\cos^2\beta}$$

Now just substitute numbers and solve...