Вычислите: а) 3 cos (π/3) − 2 sin (π/6) + 3 tg (π/4) − ctg (π/4); б) sin (−π) + 2 cos (−π/2) − 3 sin (π/4) + 3 cos (−π/4); в) 6 tg (−π/3) ctg (−π/6) + sin (−π/2) − 5 cos (−π).

а) \(\cos\frac\pi3=\frac12\), \(\sin\frac\pi6=\frac12\), \(\operatorname{tg}\frac\pi4=1\), \(\operatorname{ctg}\frac\pi4=1\).

\[3\cdot\frac12-2\cdot\frac12+3\cdot1-1=\frac32.\]

б) \(\sin(-\pi)=0\), \(\cos\left(-\frac\pi2\right)=0\), \(\sin\frac\pi4=\frac{\sqrt2}{2}\), \(\cos\left(-\frac\pi4\right)=\frac{\sqrt2}{2}\).

\[0+2\cdot0-3\frac{\sqrt2}{2}+3\frac{\sqrt2}{2}=0.\]

в) \(\operatorname{tg}\left(-\frac\pi3\right)=-\sqrt3\), \(\operatorname{ctg}\left(-\frac\pi6\right)=-\sqrt3\), \(\sin\left(-\frac\pi2\right)=-1\), \(\cos(-\pi)=-1\).

\[6\cdot(-\sqrt3)\cdot(-\sqrt3)-1-5\cdot(-1)=18-1+5=22.\]

Ответ: а) \(\frac32\); б) \(0\); в) \(22\).