sinx=3/4 x∈(π/2,π) 求sin(x+π/4) cos(x-π/3)
问题描述：
sinx=3/4 x∈(π/2,π) 求sin(x+π/4) cos(x-π/3)
答
∵sinx=3/4 ,x∈(π/2,π)
∴cosx=-√(1-sin²x)=-√7/4
sin(x+π/4)
=sinxcosπ/4+cosxsinπ/4
=3/4*(√2/2)+(-√7/4)*(√2/2)
=3√2/8-√14/8
=(3√2-√14)/8
cos(x-π/3)
=cosxcosπ/3+sinxsinπ/3
=(-√7/4)*(1/2)+3/4*(√3/2)
=-√7/8+3√3/8
=(3√3-√7)/8