- 数学加减法定理1、计算sin5π/8×cos7π/8-cos5π
- 1、计算sin5π/8×c7π/8-cos5π/8×sinπ/8
2、已知cosα=1/3,cos(α+β)=?3/5,且αβ都是锐角,求cosβ的值
- 1、计算sin5π/8×cos7π/8-cos5π/8×sinπ/8
=sin(5π/8)*cos(7π/8)-cos(5π/8)*sin(7π/8)
=sin[(5π/8)-(7π/8)]
=sin(-π/4)
=-√2/2
2、已知cosα=1/3,cos(α+β)=?3/5,且αβ都是锐角,求cosβ的值
已知α、β都是锐角
所以,α+β∈(0,180°)
已知cos(α+β)=-3/5
所以:sin(α+β)=4/5
已知cosα=1/3
所以,sinα=2√2/3
则:cosβ=cos[(α+β)-α]
=cos(α+β)*cosα+sin(α+β)*sinα
=(-3/5)*(1/3)+(4/5)*(2√2/3)
=(8√2-3)/15.