求sec50`+tan10`的值 上面的数值是度

Question

如题所述

Answer 1

sec50+tan10
=1/cos50 + sin10/cos10
=2sin50/2sin50*cos50 + sin10/cos10
=2sin50/sin100 + sin10/cos10
=2sin50/cos10 + sin10/cos10
=(2sin50+sin10)/cos10
={根据和差化积公式 sin50+sin10
=2sin(50+10)/2 * cos(50-10)/2=2sin30*cos20} (sin50+cos20)/cos10
={再用和差化积公式 sin50+cos20=cos40+cos20
=2cos(40+20)/2 * cos(40-20)/2
=cos30 * cos10 *2
=根号3 *cos10} 根号3 *cos10/cos10
=根号3
辛苦啊!