trigonometry - $(sintheta+costheta)^2=1+sin2theta$

49) $(\sin\theta+\cos\theta)^2=1+\sin2\theta$
Left Side:
$$\begin{align*} (\sin\theta+\cos\theta)^2=\sin^2\theta+2c\cos\theta\sin\theta+cos^2\theta=1+2\cos\theta\sin\theta \end{align*}$$
This can either be $1$ or I can power reduce it. I don't know.

Right Side:
$$\begin{align*} 1+\sin2\theta=1+2\sin\theta\cos\theta \end{align*}$$

Thank you!

Answer

Open parentheses and use:

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

$$(2)\,\,\sin 2x=2\sin x\cos x$$