1.cos 5/12π
=cos(1/6π +1/4π)
=cos(1/6π)cos(1/4π) — sin(1/6π)sin(1/4π)
=√3/2*√2/2 — 1/2 *√2/2
=(√6 — √2)/4
2.cos(a+b)+cos(a-b)
=cosacosb-sinasinb+cosacob+sinasinb
=2cosacosb,
所以cosacosb=1/6
3.
cosa=3/5,
sina=4/5
锐角a、b
sin(a+b)>0
cos(a+b)=-5/13
sin(a+b)=12/13
cosb=cos(a+b-a)
=cos(a+b)cosa+sin(a+b)sina
=-5/13*3/5+12/13*4/5
=33/65.
4.因为tana=1/2,cosa=1/7
所以sina=1/14cos(a-派/3
=cosacos派/3+sinasin派/3
=1/10+√3/20
=(2+√3)/20