已知a属于(π/2,π),且4sina=-3cosa,求cos(a+π/4)/sina的值

问题描述:

已知a属于(π/2,π),且4sina=-3cosa,求cos(a+π/4)/sina的值

4sina=-3cosa
sina/cosa=-3/4
tana=-3/4
cos(a+π/4)/sina
=(cosacosπ/4-sinasinπ/4)/sina
=cotacosπ/4-sinπ/4
=√2/2(1/tana-1)
=√2/2(-4/3-1)
=-7√2/6