求值:sec50°+ctg80°.
问题描述：
求值:sec50°+ctg80°.
答
sec50°+cot80°
=1/cos50°+1/tan80°
=1.555723827+0.1763269807
=1.732050808
=根号3
答
sec50+ctg80=1/cos50+tan10=1/cos50+sin10/cos10=2sin50/2sin50*cos50 + sin10/cos10=2sin50/sin100 + sin10/cos10=2sin50/cos10 + sin10/cos10=(2sin50+sin10)/cos10=sin50+sin10=2sin(50+10)/2 * cos(50-10)/2=2sin30*cos20} (sin50+cos20)/cos10= 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
答
sec50+ctg80
=csc40+ctg80
=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.