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.

for case a)
$$\sec A = 2$$
$$\cos A=\frac{1}{\sec A}=\frac{1}{2}$$
$$\sin A=\sqrt{1-\cos^2A}=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}$$
$$\tan A=\frac{\sin A}{\cos A}=\sqrt 3$$
$$\operatorname{cotg} A=\frac{1}{\tan A}=\frac{1}{\sqrt 3}$$
and for b) follow Martin Sleziak
