已知向量a=(sinx,cosx-2sinx),b=(1,2)(1)若a//b,求tanx的值.(2)若|a|=|b|,0

1.因为a平行b 所以(cosx - 2sinx) / sinx = 2 / 1 即(cosx - 2(tanx * cosx)) / (tanx * cosx) = 2 (cosx * (1 - 2tanx)) / (tanx * cosx) = 2 (1 - 2tanx) / tanx = 2 1 - 2tanx = 2tanx 4tanx = 1 tanx = 1/4 2.因为|a| = |b| 所以(sinx)^2 + (cosx - 2sinx)^2 = 1^2 + 2^2 展开为 (sinx)^2 + (cosx)^2 - 4sinx*cosx + 4(sinx)^2 = 5 1 - 4sinx*cosx + 4(sinx)^2 = 5 - 4sinx*cosx + 4(sinx)^2 = 4 - sinx*cosx + (sinx)^2 = 1 - sinx*cosx = 1 - (sinx)^2 -sinx*cosx = (cosx)^2 tanx = -(cosx)^2 / (cosx)^2 当(cosx)^2 > 0 时 tanx = -1 ;x = -45° 当(cosx)^2 = 0 时 -(cosx)^2 / (cosx)^2无意义,即tanx不存在,即x = k * pi + 90°(k为整数) 又因为0