Довести тотожнисть cos(a+60)-cos(a-60)/sin(a+60)+sin(a-60)=корень з 3

cos(a + 60) = cos(a) * cos(60) + sin(a) * sin(60) = 1/2 * cos(a) + √3/2 * sin(a);

cos(a - 60) = 1/2 * cos(a) - √3/2 * sin(a);

sin(a + 60) = sin(a) * cos(60) + cos(a) * sin(60) = 1 /2 * sin(a) +  √3/2 * cos(a);

sin(a - 60) = 1 /2 * sin(a) +  √3/2 * cos(a);

 Подставив в исходное уравнение, получим:

(cos(a) + √3sin(a)) * (sin(a) +  √3cos(a) - (1/2 * cos(a) - √3/2 * sin(a) +  (sin(a) +  √3cos(a)) * (sin(a) +  √3 * cos(a)) = √3 * (cos^2(a) + sin^2(a)) = √3.