热心网友
绝对值X小于等于45度，F（X）= (COSX)^2 + SINX的最小值F（X）= (COSX)^2 + SINX== 1 + sinx -(sinx)^2== -(sinx - 1/2 )^2 + 5/4因为 -π/4 ≤x ≤π/4所以 -√2/2 ≤sinx ≤√2/2所以 -(3-2√2)/4≤ -(sinx - 1/2 )^2 ≤ 0即 (√2+1)/2≤F（X）≤5/4所以 F（X）min = (√2+1)/2
绝对值X小于等于45度，F（X）= (COSX)^2 + SINX的最小值F（X）= (COSX)^2 + SINX== 1 + sinx -(sinx)^2== -(sinx - 1/2 )^2 + 5/4因为 -π/4 ≤x ≤π/4所以 -√2/2 ≤sinx ≤√2/2所以 -(3-2√2)/4≤ -(sinx - 1/2 )^2 ≤ 0即 (√2+1)/2≤F（X）≤5/4所以 F（X）min = (√2+1)/2