已知sin(5π-θ)+sin(5π/2-θ)=根号7/2求(1)[sin(π/2+θ)]^3-[cos(3π/2-θ)]^3(2))[sin(π/2-θ)]^4-[cos(7π/2+θ)]^4
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![已知sin(5π-θ)+sin(5π/2-θ)=根号7/2求(1)[sin(π/2+θ)]^3-[cos(3π/2-θ)]^3(2))[sin(π/2-θ)]^4-[cos(7π/2+θ)]^4](/uploads/image/z/10276714-10-4.jpg?t=%E5%B7%B2%E7%9F%A5sin%285%CF%80-%CE%B8%29%2Bsin%285%CF%80%2F2-%CE%B8%29%3D%E6%A0%B9%E5%8F%B77%2F2%E6%B1%82%EF%BC%881%29%5Bsin%28%CF%80%2F2%2B%CE%B8%EF%BC%89%5D%5E3-%5Bcos%283%CF%80%2F2-%CE%B8%29%5D%5E3%282%29%29%5Bsin%28%CF%80%2F2-%CE%B8%EF%BC%89%5D%5E4-%5Bcos%287%CF%80%2F2%2B%CE%B8%29%5D%5E4)
已知sin(5π-θ)+sin(5π/2-θ)=根号7/2求(1)[sin(π/2+θ)]^3-[cos(3π/2-θ)]^3(2))[sin(π/2-θ)]^4-[cos(7π/2+θ)]^4
已知sin(5π-θ)+sin(5π/2-θ)=根号7/2
求(1)[sin(π/2+θ)]^3-[cos(3π/2-θ)]^3
(2))[sin(π/2-θ)]^4-[cos(7π/2+θ)]^4
已知sin(5π-θ)+sin(5π/2-θ)=根号7/2求(1)[sin(π/2+θ)]^3-[cos(3π/2-θ)]^3(2))[sin(π/2-θ)]^4-[cos(7π/2+θ)]^4
根据诱导公式,sin(5π-θ)+sin(5π/2-θ)=sinθ+cosθ=根号7/2
(sinθ+cosθ)^2=7/4
(sinθ)^2+(cosθ)^2+2sinθcosθ=7/4
2sinθcosθ=3/4,sinθcosθ=3/8
(1)[sin(π/2+θ)]^3-[cos(3π/2-θ)]^3=(cosθ)^3+(sinθ)^3
=(sinθ+cosθ)[(sinθ)^2-sinθcosθ+(cosθ)^2]=(5倍根号7)/16
(2)[sin(π/2-θ)]^4-[cos(7π/2+θ)]^4=(cosθ)^4-(sinθ)^4
=[(sinθ)^2+(cosθ)^2][(sinθ)^2-(cosθ)^2]
=(sinθ+cosθ)(sinθ-cosθ)
=(sinθ+cosθ)*根号[(sinθ+cosθ)^2-4sinθcosθ]=(根号7)/4
第二问改成[sin(π/4-θ)]^4-[cos(7π/2+θ)]^4怎么做