+564 Find the exact value of sin 345 by using the identity for sin(A + B) and the fact that
345degrees= 120degree + 225degrees
+118690 $$sin345=sin(120+225)\\\\
=sin120cos225+cos120sin225\\\\
=sin60\times-cos45+-cos60\times-sin45\\\\
=\left(-\frac{\sqrt3}{2}\times\frac{1}{\sqrt2}\right)+\left(\frac{1}{2}\times\frac{1}{\sqrt2}\right)\\\\
=\frac{1-\sqrt3}{2\sqrt2}\\\\
=\frac{(1-\sqrt3)\sqrt2}{4}\\\\
=\frac{\sqrt2-\sqrt6}{4}\\\\$$
+118690 $$sin345=sin(120+225)\\\\
=sin120cos225+cos120sin225\\\\
=sin60\times-cos45+-cos60\times-sin45\\\\
=\left(-\frac{\sqrt3}{2}\times\frac{1}{\sqrt2}\right)+\left(\frac{1}{2}\times\frac{1}{\sqrt2}\right)\\\\
=\frac{1-\sqrt3}{2\sqrt2}\\\\
=\frac{(1-\sqrt3)\sqrt2}{4}\\\\
=\frac{\sqrt2-\sqrt6}{4}\\\\$$
