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!