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If x is the smallest internal angle in a triangle, then the range of the function y = SiNx + cosx is () A. [12，22]B. （0，32]C. （1，2]D. （12，22]
Because x is the smallest internal angle in a triangle, 0 ＜ x ≤ π 3Y = SiNx + cosx = 2Sin (x + π 4) ‖ π 4 ＜ π 4 + X ≤ 7 π 1222 ＜ sin (x + π 4) ≤ 11 ＜ y ≤ 2, so C is selected
If x is the minimum internal angle of a triangle, then the maximum value of the function y = SiNx + cosx + sinxcosx is ()
A. -1B. 2C. −12+2D. 12+2
Y = SiNx + cosx + sinxcosx = SiNx (1 + cosx) + 1 + cosx-1 = (1 + SiNx) (1 + cosx) - 1 ≤ 12 [(1 + SiNx) 2 + ((1 + cosx) 2] - 1 (if and only if 1 + SiNx = 1 + cosx, then SiNx = cosx = 22), that is, y (max) = 2 + 12, so D is selected
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