Question

упростить выражение.

Answer 1

Ответ:

$\dfrac{cos50\cdot (cos30\cdot cos20-sin30\cdot sin20)}{sin100}=\dfrac{cos50\cdot cos(30+20)}{sin100}=\\\\\\=\dfrac{cos^250}{2\, sin50\cdot cos50}=\dfrac{cos50}{2\, sin50}=\dfrac{ctg50^\circ }{2}$

Answer 2

$\dfrac{Cos50^\circ\cdot(Cos30^\circ Cos20^\circ-Sin30^\circ Sin20^\circ) }{Sin100^\circ}=\dfrac{Cos50^\circ \cdot Cos(30^\circ+20^\circ)}{Sin100^\circ} =\\\\=\dfrac{Cos50^\circ \cdot Cos50^\circ}{2Sin50^\circ\cdot Cos50^\circ}=\dfrac{0,5Cos50^\circ}{Sin50^\circ}=\boxed{0,5Ctg50^\circ}$