Question

已知sinθ+mcosθ=1,求msinθ-cosθ的值

Answer 1

(msinθ-cosθ)^2=(msinθ)^2-2msinθcosθ+(cosθ)^2

(sinθ+mcosθ)^2=(sinθ)^2+2msinθcosθ+(mcosθ)^2

所以(msinθ-cosθ)^2+(sinθ+mcosθ)^2=(msinθ)^2+(mcosθ)^2+(sinθ)^2+(cosθ)^2=m^2+1

又因为sinθ+mcosθ=1,所以(sinθ+mcosθ)^2=1

所以(msinθ-cosθ)^2=（m^2+1）-1=m^2

所以·msinθ-cosθ=m或-m