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![\bf \begin{array}{llll} \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \end{array}\qquad \qquad \qquad \begin{array}{llll} \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta) \end{array}\\\\ -------------------------------\\\\ \begin{cases} t=cos(A)+sin(A)\\ t^2=[cos(A)+sin(A)]^2 \end{cases}\implies \stackrel{FOIL}{cos^2(A)+2cos(A)sin(A)+sin^2(A)} \\\\\\ \boxed{sin^2(A)+cos^2(A)}+2cos(A)sin(A)\implies \boxed{1}+2sin(A)](/tpl/images/0087/9077/b60d1.png)
and the double angle formula for sine, 
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