已知cos（75°+θ）=1/3,θ为第三象限角,求值：cos(-255°-θ）+sin(435°+θ）

Question

已知cos（75°+θ）=1/3,θ为第三象限角,求值：cos(-255°-θ）+sin(435°+θ）

Answer 1

cos(-255°-θ)+sin(435°+θ)=cos(255°+θ)+sin(360°+75°+θ) =cos(180°+75°+θ)+sin(75°+θ) =-cos(75°+θ)+sin(75°+θ) θ为第三象限角,75°+θ为第三或第四象限角 sin(75°+θ)=-根号(1-cos^2[(75°+θ)])=-(2根号2)/3 cos(-255°-θ)+sin(435°+θ)=-1/3-(2根号2)/3