Value of $\cos^2\alpha-\sin^2\alpha$ My problem is from Israel Gelfand's Trigonometry textbook.
Page 48. Exercise 8: b) If $\tan\alpha=r$, write an expression in terms of $r$ that represents the value of $\cos^2\alpha-\sin^2\alpha$.
The attempt at a solution:
Well I solved a) which was similar, question was: a) If $\tan\alpha=2/5$, find the numerical value of $\cos^2\alpha-\sin^2\alpha$. Solution was this, since $\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{2}{5}$, then $\cos^2\alpha-\sin^2\alpha=5^2-2^2=21$. b) part is more general version of a) I guess, but I can't seem to find identity that would allow me to solve it. I would appreciate some hints, thank you in advance.

Two Hints:
$$\cos^2 x = \frac{\cos^2x}{1}=\frac{\cos^2x}{\sin^2 x+\cos^2 x}=\frac{1}{\tan^2 x+1}$$
And:
$$\cos^2 x - \sin^2 x=\cos^2 x-\sin^2 x +(\cos^2x +\sin^2x)-1=2\cos^2x-1$$
