Question

方程sinx+cosx=sqr(2)/2在区间【0,4π】上所有解的和是

Answer 1

sinx+cosx= 根号2 sin(x+PI/4) = 根号2 / 2

x + PI/4 = PI/6,或 PI / 6 +2 PI

x = PI/12,或 PI/12 + 2PI

和为 PI/6 + 2 PI