# Math Help - help with some questions

1. ## help with some questions

I am having trouble with some of these questions:

1. 2 tan (5pi/8) = tan 5pi/4 (use the double angle formula, but what is the answer)?

And ...

2. Express tan in terms of cosine and sine.

Do I use the Pythagorean identity? (1 + tan^2x = sec^2x and 1 + cot^2x = cot^2x)

2. 1) The equality is wrong.

$\tan 2x=\frac{2\tan x}{1-\tan^2x}$

Then
$\tan\frac{5\pi}{4}=\tan\left(2\cdot\frac{5\pi}{8}\ right)=\frac{2\tan\frac{5\pi}{8}}{1-\tan^2\frac{5\pi}{8}}$

2)
$\tan x=\frac{\sin x}{\cos x}=\pm\frac{\sqrt{1-\cos^2x}}{\cos x}$

$\tan x=\frac{\sin x}{\cos x}=\pm\frac{\sin x}{\sqrt{1-\sin^2x}}$