Question

高中三角函数一道题

求值：（2sin80°-cos70°）/cos20°

Answer 1

(2sin80-cos70)/cos20
=[2sin(60+20)-sin20]/cos20
=[2(sin60cos20+cos60sin20)-sin20]/cos20
=(2sin60cos20+2cos60sin20-sin20)/cos20
因为cos60=1/2
所以，原式=(2sin60cos20+2×1/2sin20-sin20)/cos20
=(2sin60cos20+sin20-sin20)/cos20
=(2sin60cos20)/cos20
=2sin60
=2×√3/2
=√3

祝您学习愉快