化简求值sin(-20/3π)cos(43/6π)+sin(35/6π)cos-(17/3π)

题目

化简求值sin(-20/3π)cos(43/6π)+sin(35/6π)cos-(17/3π)
sin(-20/3π)cos(43/6π)+sin(35/6π)cos-(17/3π)
[2sin50°+cos10°(1+根号（3）tan10°)]/根号(1+cos10°)

答案

sin(-20/3π)cos(43/6π)+sin(35/6π)cos-(17/3π)
=sin(-2/3π)cos(7/6π)+sin(-1/6π)cos(1/3π)
=sin(1/3π)cos(1/6π)-sin(1/6π)cos(1/3π)
=sin(1/3π-1/6π）=-1/2
[2sin50°+cos10°(1+根号（3）tan10°)]/根号(1+cos10°)
=[2sin50°+cos10°+根号（3）sin10°)]/(根号(2)cos5°)
=[2sin50°+2(cos60°cos10°+sin60°sin10°)]/(根号(2)cos5°)
=[2sin50°+2cos50°]/(根号(2)cos5°)
=[2根号（2）cos5°]/(根号(2)cos5°)
=2