高一数学必修四三角函数题若sin (π+α)-cos(-α)=1/2则sin^3 (π+α)+cos^3 (2π+α)的值是?
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高一数学必修四三角函数题若sin (π+α)-cos(-α)=1/2则sin^3 (π+α)+cos^3 (2π+α)的值是?
高一数学必修四三角函数题
若sin (π+α)-cos(-α)=1/2
则sin^3 (π+α)+cos^3 (2π+α)的值是?
高一数学必修四三角函数题若sin (π+α)-cos(-α)=1/2则sin^3 (π+α)+cos^3 (2π+α)的值是?
sin (π+α)-cos(-α)=1/2
则-sin α-cosα=1/2
sin α+cosα=-1/2
(sin α+cosα)^2=1/4=1+2sin αcosα
sin αcosα=-3/8
sin α^2+cosα^2-2sin αcosα=7/4
(sin α-cosα)^2=7/4
sin α-cosα=正负(根7)/2
sin^3 (π+α)+cos^3 (2π+α)=-sin^3 α+cos^3 α=-(sin α-cosα)(1+sin αcosα)
=正负5(根7)/16
sin (π+α)-cos(-α)=1/2
-sinα- cos(-α)=1/2
sinα+cos α=-1/2
(sinα+cos α)2=1/4
Sin2α+cos2 α+2sinαcosα=1/4
sinαcosα=-3/8
√2/2 sinα+√2/2 cos α=-1/2×√2/2
sin(α+π/4) =-√2/4
cos...
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sin (π+α)-cos(-α)=1/2
-sinα- cos(-α)=1/2
sinα+cos α=-1/2
(sinα+cos α)2=1/4
Sin2α+cos2 α+2sinαcosα=1/4
sinαcosα=-3/8
√2/2 sinα+√2/2 cos α=-1/2×√2/2
sin(α+π/4) =-√2/4
cos (α-π/4)= -√2/4
sin3 (π+α)+cos3(2π+α)
=(-sinα)3+ (cosα)3
=(cosα)3- (sinα)3
=( cosα- sinα)( cos2α+ sin2α- cosαsinα)
= cos (α-π/4) (1- cosαsinα)
= -√2/4×11/8
=-11√2/32
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