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Prove that：tan-11/3+tan-11/5+tan-11/7+tan-11/8=45°
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Prove that：(sin75°+sin15°)/(sin75°-sin15°)=tan60°
Given ∠1=∠2,a,b,c，find d.
Transform the difference of two squares into a rectangle, the ratio of two sides being 2 : 3.
With BC, one leg of △ABC, as diameter, a circle is described intersecting the hypotenuse AC at P. From P draw a tangent intersecting AB at D. Showt hat AD = BD.
Show that the line joining the mid-points of the diagonals of a trapezoid is half the difference of its bases.
Evaluate to four significant figure by logarithm,
Simplify yz(x+a)/(x-y)(x-z)+zx(y+a)/(y-z)(y-x)+xy(z+a)/(z-x)(z-y)
Determine the real value of k, so that the roots of equation, (k - 1)x² - kx - 2x + 4 = 0, may be real and equal.
Solve and verify x²+3x-6(x²+3x-3)1/2+2=0
圣约翰大学幂函数
求证下列恒等式tan-1m+tan-1n=tan-1(m+n)/(1-mn)
试证下列恒等式2 sec-1x=tan-1
设α=4π/3，则arccos(cosα)的值是【 】
设 |a|≤1，求arccosa+arccos(-a)的值.
当x∈[0,1]时，在下面关系式中正确的是【 】
函数y=arcsinx(x∈[-1,1])的反函数是__________.
函数y=arccos(sinx)(- π/3<x<2π/3)的值域是【 】
使arcsinx>arccosx成立的x的取值范围是【 】
若0<α<π/2，则acrsin[cos(π/2+a) ]+arccos[sin(π+α) ]等于【 】
满足arccos(1-x)≥arccos的x的取值范围是【 】
已知f(x)=1/2 sin2x，关于该函数的四个说法：①f(x)的最小正周期为2π；②f(x)在[-π/4,π/4]上单调递增；③当x∈[-π/6,π/3]时，f(x)的取值范围为[-√3/4,√3/4]；④f(x)的图像可由g(x)=1/2 sin(2x+π/4)向左平移π/8个单位长度得到.正确的个数有【 】个
已知tanθ<0,cos(π/2+θ)=√5/5，则cosθ的值为【 】
证(tan2x-tan2y)/sec2xsec2y=sin(x+y)sin(x-y).
tan30°=______.
tan45°=______.
tan60°=______.
对于-π/4<β<0<α<π/4，已知sin(α+β)=1/3,cos(α-β)=2/3，则不大于(sinα/cosβ+cosβ/sinα+cosα/sinβ+sinβ/cosα)²的最大整数为______.
设 A+B + C =180°，试证 sin2A +sin2B +sin2C = 4sinAsinBsinC.
证cosθ=4 cos³(θ/3)-3 cos(θ/3).
设函数 f(x) = cos (ωx + π/6 ) 在 [−π, π] 的图像大致如下图, 则 f(x) 的最小正周期为【 】。
