求值：（-根号3）*tan20+4cos70,问题应该是..........求值：（-根号3）*tan70°+4cos20

Question

求值：（-根号3）*tan20 +4cos70 ,
问题应该是..........求值：（-根号3）*tan70° +4cos20

Answer 1

- √3 tan70° + 4cos20°
= 4cos20° - √3 cot20°
= 4cos20 - √3 cos20/sin20
= (4cos20sin20 - √3cos20) / sin20
= (2sin40 - √3cos20) / sin20
= [ 2(sin60-20) - √3cos20] / sin20
= [ 2sin60cos20 - 2cos60sin20 - √3cos20] / sin20
= [ √3cos20 - sin20 - √3cos20] / sin20
= - 1