已知cos(75°+θ)=1/3,θ为第三象限角,求cos(-225°-θ)+sin(435°+θ)的值.

cos(75°+θ)=1/3,θ为第三象限角
设 75°+θ=A
∴ θ=A-75°
则 cosA=1/3, A是第四象限角
∴ sinA=-√(1-cos²A)=-2√2/3
cos(-225°-θ)+sin(435°+θ)
=cos(225°+θ)+sin(435°+θ)
=cos(225°+A-75°)+sin(435°+A-75°)
=cos(150°+A)+sin(360°+A)
=cos150°cosA-sin150°sinA+sinA
=(-√3/2)*(1/3)-(1/2)*(-2√2/3)+(-2√2/3)
=-√3/6 -2√2/3

cos(-225°-θ)+sin(435°+θ)=cos[-（225°+θ）]+sin[90*4+75+θ]=cos(180°-30°+75°+θ)+sin(75°+θ)
因为cos(75°+θ)=1/3,θ为第三象限角，所以sin(75°+θ)=-根号2/3.cos(180°-30°+75°+θ)=cos【180°-（30°-75°-θ)]=-cos（30°-75°-θ)=-cos[30...