Question

cos50°×(cos30°cos20°-sin30°sin20°)/sin100°
$\frac{cos50 \times (cos30 \times cos20 - sin30 \times sin20)}{sin100}$
ХЭЛП​

Answer 1

Решение.

$\bf \dfrac{cos50^\circ (cos30^\circ \, cos20^\circ -sin30^\circ \, sin20^\circ )}{sin100^\circ }=$

 Воспользуемся формулой косинуса суммы:

$\bf cos(a+\beta )=cosa\cdot cos\beta -sina\cdot sin\beta$

$\bf =\dfrac{cos50^\circ \cdot cos(20^\circ +30^\circ )}{sin100^\circ }=\dfrac{cos50^\circ \cdot cos50^\circ }{sin(2\cdot 50^\circ )}=\dfrac{cos50^\circ \cdot cos50^\circ }{2\cdot sin50^\circ \cdot cos50^\circ }=\\\\\\=\dfrac{cos50^\circ }{2\cdot sin50^\circ }=\dfrac{1}{2}\cdot ctg50^\circ$