+
=1/cos50+sin10/cos10
=2sin50/sin100+sin10/cos10
=[2sin(60-10)+sin10]/cos10
=(2sin60cos10-2cos60sin10+sin10)/cos10
=√3cos10/cos10
=√3.
=csc40+cot80
=1/sin40+cos80/sin80
=1/sin40+cos80/(2sin40cos40)
=(2cos40+cos80)/sin80
=(cos80+cos40+cos40)/sin80
=(2cos60cos20+cos40)/sin80
=(cos20+cos40)/sin80
=2cos30cos10/cos10
=2cos30
=√3.
sec50度+tan10度=1/(cos50)+sin10/(cos10)
=(cos10+sin10*cos50)/(cos50*cos10)
∵sinα*cosβ=1/2[sin(α+β)+sin(α-β)]
cosα*cosβ=1/2[cos(α+β)+cos(α-β)]
∴cos10+sin10*cos50
=cos(40-30)+1/2[sin(10+50)+sin(10-50)]
=cos40*cos30+sin40*sin30+1/2sin60-1/2sin40
=(√3/2)cos40+1/2sin40+√3/4-1/2sin40
=(√3/4)(2cos40+1)
cos50*cos10
=1/2[cos(50+10)+cos(50-10)]
=1/2[cos60+cos40]
=1/2(1/2+cos40)
=1/4(2cos40+1)
∴sec50度+tan10度
=(cos10+sin10*cos50)/(cos50*cos10)
=√3tan10度等于多少。
注意:度的单位省略。
希望你能看明白。