几道小题目

Question

(1)sin13cos17+cos13sin17化简得A根号3/2 B0.5 Csin4 Dcos4
(2)sin200cos140-cos160sin40化简得A根号3/2 Bsin20 Ccos20 D0.5
(3)sin11cos29+cos11sin29
(4)cos24cos69+sin24sin111
(5)(sin22.5)^2-(cos22.5)^2
(6)2sin15cos15
(7)sin105
(8)cos165

Answer 1

(1)sin13cos17+cos13sin17
=sin(13+17)
=sin30
=1/2
A根号3/2 B0.5 Csin4 Dcos4
选B

(2)sin200cos140-cos160sin40
=sin(180+20)cos(180-40)-cos(180-20)sin40
=sin20cos40+cos20sin40
=sin(20+40)
=sin60
A根号3/2 Bsin20 Ccos20 D0.5
选A

(3)sin11cos29+cos11sin29
=sin(11+29)
=sin40

(4)cos24cos69+sin24sin111
=cos24cos69+sin24sin(180-69)
=cos24cos69+sin24sin69
=cos(24-69)
=cos(-45)
=cos45
=根号2/2

(5)(sin22.5)^2-(cos22.5)^2
=-[(cos22.5)^2-(sin22.5)^2]
=-cos(22.5+22.5)
=-cos45
=-根号2/2

(6)2sin15cos15
=sin30
=1/2

(7)sin105
=sin(45+60)
=sin45cos60+cos45sin60
=√2/4+√6/4
=(√2+√6)/4

(8)cos165
=cos(180-15)
=-cos15
=-cos(45-30)
=-cos45cos30+sin45sin30
=-√6/4+√2/2
=(√2-√6)/2