Question

Упростите выражение

$frac{10sin40*sin50}{cos10}$

 

 

Answer 1

sina*sinb=1/2[cos(a-b)-cos(a+b)]
10(1/2 * (cos(50-40) - cos(50+40))/cos 10 = 5*(cos10 - 0) / cos 10 = 5

Answer 2

$frac{10sin40sin50}{cos10}=frac{10cdot frac{1}{2} (cos(40-50)-cos(40+50))}{cos10}=frac{5 (cos10-cos90)}{cos10}=frac{5cos10}{cos10}=5$