sin(30'+a)=1/3,求cos(120'-2a)的值

sin(30'+a)=1/3,求cos(120'-2a)的值
sin(30'+a)=1/3,求cos(120'-2a)的值

sin(30'+a)=1/3,求cos(120'-2a)的值
cos(2a+60)
=cos[2(a+30)]
=1-2sin²(a+30)
=7/9
cos(120-2a)
=cos[180-(2a+60)]
=-cos(2a+60)
=-7/9

sin(30'+a)=1/3
cos(120'-2a)
利用 诱导公式
=cos(60'+2a)
利用二倍角公式
=1-2sin²(30'+a)
=1-2*(1/3)²
=1-2/9
=7/9

111

cos(120°-2a)
=cos[180-(2a+60°)]
=-cos(2a+60)
=-cos2(a+30°)
=-[1-2sin²(a+30°)]
=-1+2sin²(a+30°)
=-1+2/9
=-7/9