✔ 最佳答案
1)
f(x)= cos^2x-sinx+1= (1 - sin^2 x) - sinx + 1= - sin^2 x - sinx + 2= - (sin^2 x + 2(1/2)sinx + (1/2)^2 - (1/2)^2) + 2= - [ (sin x + 1/2)^2 - 1/4 ] + 2= - (sin x + 1/2)^2 + 9/4 ;- 1 =< sin x =< 1當 sin x = - 1/2 , 最大值 M = 9/4
當 sin x = 1 , 最小值 m = - (3/2)^2 + 9/4 = 0M + m = 9/4 + 0 = 9/42) (tanθ + secθ + 1) (cotθ - cscθ + 1)= (sinθ/cosθ + 1/cosθ + 1) (cosθ/sinθ - 1/sinθ + 1)= [(sinθ + cosθ + 1) / cosθ] [sinθ + cosθ - 1) / sinθ]= [(sinθ + cosθ )^2 - 1] / (sinθ cosθ)= (sin^2 θ + cos^2 θ + 2 sinθ cosθ - 1) / (sinθ cosθ)= 2 sinθ cosθ / (sinθ cosθ)= 2
2010-11-10 12:44:49 補充：
你知道是sinθ/cosθ+cosθ+1/cosθ ,
其實不對 ,應是
(sinθ/cosθ + 1/cosθ + 1) (cosθ/sinθ - 1/sinθ + 1)
= (sinθ/cosθ + 1 + 1/cosθ) (cosθ/sinθ + 1 - 1/sinθ )
= (sinθ/cosθ + cosθ/cosθ + 1/cosθ) (cosθ/sinθ + sinθ/sinθ - 1/sinθ )
(1 是 cosθ/cosθ 不是 cosθ)
= [(sinθ + cosθ + 1) / cosθ] [(cosθ + sinθ - 1) / sinθ)
