Question

How do you prove `\sin ^ { 2} \theta - \cos ^ { 2} \theta = \cos \theta + 1`?

Answer 1

It cannot be proven. It is not always true.

Explanation:

Counterexample: with `theta = pi/4` (or `45^@`) we have

`sin^2(pi/4)-cos^2(pi/4) = 0`

But `cos (pi/4) + 1 = sqrt2/2+1 != 0`