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(1+sin a + cos a)(sin a + cos a - 1)

Answer 1

$\displaystyle\bf\\(1+Sin\alpha +Cos\alpha )(Sin\alpha +Cos\alpha -1)=\\\\=\bigg[(Sin\alpha +Cos\alpha)+1 \bigg]\bigg[(Sin\alpha +Cos\alpha) -1\bigg]=(Sin\alpha +Cos\alpha )^{2} -1^{2} =\\\\=Sin^{2} \alpha +2Sin\alpha Cos\alpha +Cos^{2} \alpha -1=\underbrace{Sin^{2} \alpha +Cos^{2} \alpha}_{1} +\underbrace{2Sin\alpha Cos\alpha}_{Sin2\alpha }-1=\\\\=1+Sin2\alpha -1=Sin2\alpha$