Question

sin(170)-cos(10)=??
Multumesc!

Answer 1

$sin(\pi-x)=sin\pi\cdot cosx-cos\pi\cdot sinx=0\cdot cosx-(-1)\cdot sinx=sinx\\sin(170^{\circ})=sin(180^\circ-170^\circ)=sin10^\circ\\sin10^\circ-cos10^\circ=sin10^\circ-sin(90^\circ-10^\circ)=sin10^\circ-sin80^\circ=\\=2\cdot sin\frac{10^\circ-80^\circ}{2}\cdot cos\frac{10^\circ+80^\circ}{2}=-2\sin35^\circ\cdot cos45^\circ=-\sqrt2\cdot sin35^\circ.$