Question

两道数学题，急需，在线等

1.sin113°cos22°+sin203°sin158°=？
2.已知cos（a-π/3)=12/13,π/3<a<π/2,求cosa

Answer 1

1.sin113°cos22°+sin203°sin158°
==cos23cos22-sin23sin22
=cos45
=√2/2

2.已知cos（a-π/3)=12/13,π/3<a<π/2,求
cos（a-π/3)=5/13
cosa=cos[(a-π/3)+π/3]
=cos(a-π/3)cosπ/3-sin(a-π/3)sinπ/3
=5/13*1/2-12/13*√3/2
=(5-12√3)/26

Answer 2

1.
解：sin113°cos22°+sin203° sin158°
sin113°=cos23°，sin203°=－sin23°，sin158°=sin22°，
∴sin113°cos22°+sin203°sin158°
=cos23°cos22°－sin23°sin22°
=cos45°=

2.
cos(a-π/3)=12/13
sin(a-π/3)=5/13
cosa=cos(a-π/3)cos(π/3)-sin(a-π/3)sin(π/3)
=12/13*1/2-5/13*√3/2
=(12-5√3)/26

Answer 3

1.sin(90+23)cos22+sin(180+23)sin(180-22)=cos23cos22-sin23sin22=cos45
2刚才看错了，不好意思。