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[latex]1)\; \; cos(-\frac{\pi}{3})=cos\frac{\pi}{3}=\frac{1}{2}\\\\2sin\, 0^\circ+3cos60^\circ=2\cdot 0+3\cdot \frac{1}{2}=1,5\\\\2)\; \; sina=0,6\\\\\frac{\pi}{2}\ \textless \ a\ \textless \ \pi \; \; \to \; \; cosa\ \textless \ 0\\\\cosa=-\sqrt{1-sin^2a}=-\sqrt{1-0,36}=-0,8\\\\ctg(\frac{\pi}{2}-a)=tga= \frac{sina}{cosa} =\frac{0,6}{-0,8}=-\frac{3}{4}=-0,75\\\\3)\; \; a)\; \; tga\cdot ctga+1=1+1=2\\\\b)\; \; tg(-a)\cdot ctga+sin^2(-a)=-tga\cdot ctga+(sin(-a))^2=\\\\=-1+(-sina)^2=-1+sin^2a==-(1-sin^2a)=-cos^2a[/latex] [latex] \frac{1}{cos \beta } -cos \beta = \frac{1-cos^2 \beta }{cos \beta } = \frac{sin^2 \beta }{cos \beta } = \frac{sin \beta }{cos \beta }\cdot sin \beta =tg \beta \cdot sin \beta [/latex]