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[latex]1)\; \; sin33\, cos63-cos33\, sin63=sin(33-63)=\\\\=sin(-30)=-sin30=-\frac{1}{2}\\\\2)\; \; cos2a\cdot cos3a+sin2a\cdot sin3a=cos(3a-2a)=cosa\\\\3)\; \; cosa= \frac{2}{5}\; ,\\\\\frac{3\pi}{2}\ \textless \ a\ \textless \ 2\pi \; \; \Rightarrow \; \; sina\ \textless \ 0 \; \; \Rightarrow \; \; sina=-\sqrt{1-cos^2a}\\\\sina=-\sqrt{1-\frac{4}{25}}=-\sqrt{\frac{21}{25}}=-\frac{\sqrt{21}}{5}\\\\sin(\frac{\pi}{3}+a)=sin\frac{\pi}{3}\cdot cosa+cos\frac{\pi}{3}\cdot sina=[/latex] [latex]=\frac{\sqrt3}{2}\cdot \frac{2}{5}+\frac{1}{2}\cdot (-\frac{\sqrt{21}}{5})=\frac{2\sqrt3-\sqrt{21}}{10} [/latex] [latex]4)\; \; cos(\frac{3\pi}{2}-a)=cos\frac{3\pi}{2}\cdot cosa+sin\frac{3\pi}{2}\cdot sina=\\\\=0\cdot cosa+(-1)\cdot sina=-sina[/latex]