trigonometry - Trouble with a Trig Identity and Euler's Formula

I have the following expression

$\cos^2(s) + 2\sin^2(s)$

and need to show that it is equivalent to the following expression

$1 + \sin^2(s)$

I have no idea where to start, however. I'm familiar with the use of Euler's Formula to derive the angle addition and subtraction formulas--and from there, the double and half angle formulas.

Where do we start to go from the first statement above to the second? Can you tie the trig identities you use back to Euler's Formula?

Answer

$$\cos^2(x) + 2\sin^2(x) = \cos^2(x) + \underbrace{\sin^2(x) + \sin^2(x)}_{2\sin^2(x)}$$

Now, since $\cos^2(x) + \sin^2(x) = 1$

you easily get

$$1 + \sin^2(x)$$