Trigonometric functions of the acute angle Find the other five trigonometric functions of the acute angle A, given that:
\begin{align}
&\text{a)}\ \ \sec A = 2  \\[15pt]
&\text{b)}\ \ \cos A = \frac{m^2 - n^2}{m^2 + n^2}
\end{align}
Help me. I don't know how to solve this one. Thanks.

It is useful to know at least some basic trigonometric identities. See List of trigonometric identities at Wikipedia for a very complete list.

a) Since $\cos A=\frac1{\sec A}$, you get $\cos A=\frac12$. Can you get possible values of $A$ from there?

b) If $$\cos A=\frac{m^2-n^2}{m^2+n^2}=\left(\frac m{\sqrt{m^2+n^2}}\right)^2-\left(\frac n{\sqrt{m^2+n^2}}\right)^2,$$ then for an angle $B$ such that $\cos B=\frac m{\sqrt{m^2+n^2}}$ and $\sin B=\frac m{\sqrt{m^2+n^2}}$ you get $$\cos A=\cos^2B-\sin^2B=\cos2B.$$ Maybe this could help to express $A$ using $B$. You should be able to find $B$ using some inverse trigonometric functions. Double angle formulae should help you to get the values of $\sin A$, $\tan A$, etc for $A=2B$. (You should also think about the possibility $A=-2B$. Do you know why?)
