化简：cos(π/3+α)+sin(π/6+α)

高一上的数学题 麻烦各位帮个忙 要详细一点的过程！！！！谢谢谢谢！

这个可以用和差化积的，只不过要先用诱导公式变一下：
比如说都变成sin的
原式=sin(π/6-α)+sin(π/6+α）
=2sin0.5*[(π/6-α)+(π/6+α)] cos0.5[(π/6-α)-(π/6+α)]
=2sin π/6 cosα
=cosα

sin²α+cosαcos(π/3+α)-sin²(π/6-α) =sin²α+cosαcos(π/3+α)-cos²(π/3+α)

=sin²α+[cosa-cos(π/3+α)]cos(π/3+α)

=sin²α-2sin(-π/6)sin(π/6+α)(cos(π/3+α)

=sin²α+sin(π/6+α)(cos(π/3+α)

=sin²α+sin(π/2+2α)/2+sin(-π/6)/2

=sin²α+cos2α/2-1/4

=1-1/2-1/4

=1/4

2.求值：[sin50°（1+√3tan10°）-cos20°]/（cos80°√(1-cos20°)）

=(sin50+√3tan10sin50-cos20)/(cos80√(1-(1-2sin^2 10))

=(cos40+√3tan10sin50-cos20)/(cos80√2sin10)

=(-2sin30sin10+√3tan10sin50)/(√2cos80sin10)

=(-2sin30sin10+√3tan10sin50)/(√2cos80sin10)

=(-2sin30sin10+√3tan10sin50)/(√2cos80sin10)

=(-2sin30+√3sin50/cos10)/(√2cos80)

=(-2sin30cos10+√3sin50)/(√2sin10cos10)

=(-2sin30cos10+2cos30sin50)/(√2/2sin20)

=√2(-(sin40+sin20)+(sin20+sin80))/sin20

=√2(sin80-sin40)/sin20

=2√2(cos60sin20)/sin20

=√2

cos(π/3+α)+sin(π/6+α) =cosπ/3cosα-sinπ/3sinα+sinπ/6cosα+cosπ/6sinα =1/2*cosα-√3/2*sinα+1/2*cosα+√3/2sinα =cosα

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