Question

Если cosx+cosy=a и sinx+siny=b
Найдите cos(a+b)​

Answer 1

sinx+siny = 2sin(x + y)/2*cos(x - y)/2

cosx+cosy = 2cos(x+y)/2*cos(x - y)/2

cos 2x = (1 - tg² x) /  (1 + tg² x)

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sinx + siny = b  

cosx + cosy = a ≠ 0

делим первое на второе  

(sinx + siny)/(cosx + cosy) = b/a  

2sin(x + y)/2*cos(x - y)/2 / 2cos(x + y)/2*cos(x - y)/2 = b/a

sin(x + y) / cos(x + y)/2 = b/a  

tg(x + y)/2 = b/a

cos(x + y) =(1 - tg²(x + y)/2)  / (1 + tg²(x + y)/2) = (1  -b²/a²) / (1 + b²/a²) = (a² - b²)/a² : (a² + b²)/a² = (a² - b²) / (a² + b²)

cos(x + y) = (a² - b²) / (a² + b²)

cos(a+b)​  найти невозможно