化简sin(2-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)

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化简sin(2-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)
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化简sin(2-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)
化简sin(2-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)

化简sin(2-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)
sin(α-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)
=sinα+cosα+tanα-cosα-sinα
=tanα
一般地,加减角的2π倍函数名不变,符号不变.
更一般地,如果是π/2的整数倍,可以利用“奇变偶不变,符号看象限”来进行记忆.
即π/2的奇数倍函数名不变,偶数位则函数名改变.
符号要看变化前角所在的象限,如sin(π/2+α)
π/2是π/2的奇数倍,函数名化为cos,再看π/2+α所在的象限（把α看作锐角）,则π/2+α在第二象限,第二象限,sin为正,因此sin(π/2+α)=cosα.

sin(α-2π)+cos(2π+α)+tan(α-4π)-cos(10π+α)-sin(α-12π)
=sinα+cosα+tanα-cosα-sinα
=tanα

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