sin(x+π/3)*sin(x+π/2)的最小正周期,

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sin(x+π/3)*sin(x+π/2)的最小正周期,
sin(x+π/3)*sin(x+π/2)的最小正周期,

sin(x+π/3)*sin(x+π/2)的最小正周期,
方法一: f(x) = cos [π / 2 - (x + π / 3)] cos [π / 2 - (x + π / 2)] = cos (π / 6 - x) cos (-x) = (√3 / 2 cos x + 1 / 2 sin x) cos x =√3 / 2 (cos x)^2 + 1 / 2 sin x cos x =√3 / 4 2 (cos x)^2 + 1 / 4 2 sin x cos x =√3 / 4 [1 + cos (2 x)] + 1 / 4 sin (2 x) =√3 / 4 + 1 / 2 [√3 / 2 cos (2 x) + 1 / 2 sin (2 x) =√3 / 4 + 1 / 2 sin (2 x + π / 3) 2π / 2 = π , 所以,f(x)的最小正周期是 π. 方法二: f(x) = sin (x + π / 3) cos [π / 2 - (x + π / 2)] = sin (x + π / 3) cos (-x) = sin (x + π / 3) cos x = sin [(x + π / 6) + π / 6] cos [(x + π / 6) - π / 6] = [√3 / 2 sin (x + π / 6) + 1 / 2 cos (x + π / 6)] [√3 / 2 cos (x + π / 6) + 1 / 2 sin (x + π / 6)] = 3 / 4 sin (x + π / 6) cos (x + π / 6) +√3 / 4 [cos (x + π / 6)]^2 + √3 / 4 [sin (x + π / 6)]^2 + 1 / 4 cos (x + π / 6) sin (x + π / 6) = (3 / 4 + 1 / 4 ) sin (x + π / 6) cos (x + π / 6) + √3 / 4 {[cos (x + π / 6)]^2 + [sin (x + π / 6)]^2} = 1 / 2 2 sin (x + π / 6) cos (x + π / 6) + √3 / 4 = 1 / 2 sin (2 x + π / 3) + √3 / 4 所以,f(x)的最小正周期是 π.

sin^2(π/3-x)+sin^2(π/6+x) 化简 sin²x+sin²(x+2π/3)+sin²(x-2π/3) 2sin(x+π/4)sin(x-π/4)=? sin^2(π/4 +x) sin(πx/2)求导 sin(x+π/3)用诱导公式化简如题sin(2x+π/3)和3sin(2x+π/3) 已知sin(x+π/6)=1/3,求sin(5π/6-x)+sin^2(π/3-x) 已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x) 若tanx=2,则2sin平方x-3sin（π-x）sin（π/2-x）= sin(3π/2-x)化简 sinx>sin(2π/3-x)（0 解不等式sin(2x+π/3) sin(x+π/4) 已知函数f(x)=2根号3sin平方x-sin（2x-π/3) 化简2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1 当x趋向π lim (sin 3x )/( sin 2x) 的极限为? 化简:(sinα-cosα)^2+sin4α/2cos2α 化简:sin^2x+sin^2(x+2π/3)+sin^2(x-2π/3) 求sin^2(2x+π/3)的导数这样写为什么不对：[sin^2(2x+π/3)]'=[sin(2x+π/3)·sin(2x+π/3)]'=2[sin(2x+π/3)]'·sin(2x+π/3)=2cos(2x+π/3)·sin(2x+π/3)=sin(4x+2π/3)