531. Вычислить: 1) cos(23π/4) − sin(15π/4) − ctg(−11π/2); 2) sin(25π/3) − cos(−17π/2) − tg(10π/3); 3) sin(−7π) − 2 cos(31π/3) − tg(7π/4); 4) cos(−9π) + 2 sin(−49π/6) − ctg(−21π/4).

1) \(\cos\frac{23\pi}{4}=\cos\frac{7\pi}{4}=\frac{\sqrt2}{2}\), \(\sin\frac{15\pi}{4}=\sin\frac{7\pi}{4}=-\frac{\sqrt2}{2}\), \(\operatorname{ctg}(-\frac{11\pi}{2})=0\).

\(\frac{\sqrt2}{2}-(-\frac{\sqrt2}{2})-0=\sqrt2\).

2) \(\sin\frac{25\pi}{3}=\sin\frac{7\pi}{3}=\frac{\sqrt3}{2}\), \(\cos(-\frac{17\pi}{2})=0\), \(\operatorname{tg}\frac{10\pi}{3}=\operatorname{tg}\frac{\pi}{3}=\sqrt3\).

\(\frac{\sqrt3}{2}-0-\sqrt3=-\frac{\sqrt3}{2}\).

3) \(\sin(-7\pi)=0\), \(\cos\frac{31\pi}{3}=\cos\frac{\pi}{3}=\frac12\), \(\operatorname{tg}\frac{7\pi}{4}=-1\).

\(0-2\cdot\frac12-(-1)=0\).

4) \(\cos(-9\pi)=-1\), \(\sin(-\frac{49\pi}{6})=\sin(-\frac\pi6)=-\frac12\), \(\operatorname{ctg}(-\frac{21\pi}{4})=\operatorname{ctg}\frac{3\pi}{4}=-1\).

\(-1+2\cdot(-\frac12)-(-1)=-1\).

Ответ: 1) \(\sqrt2\); 2) \(-\frac{\sqrt3}{2}\); 3) \(0\); 4) \(-1\).