sin(a)= (2tan(a/2))/(1+tan^2(a/2)) ,cos(a)= (1-tan^2(a/2))/(1+tan_数学解答

sin(a)= (2tan(a/2))/(1+tan^2(a/2)) ,cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2)) 求sina-cosa=
why
A.sin(a-π/4)B.COS（a-π/4）C.根号2 sin(a-π/4)D.根号2COS（a-π/4）

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解答

sina-cosa= (2tan(a/2))/(1+tan^2(a/2)) - (1-tan^2(a/2))/(1+tan^2(a/2))
= (tan^2(a/2)+2tan(a/2)-1)/(1+tan^2(a/2))