Question

已知cos(π/4+x)=3/5 求sin2x的值

Answer 1

cos(π/4+x)=cosπ/4cosx-sinπ/4sinx=(1/√2)(cosx-sinx)=3/5,
cosx-sinx=3√2/5,两边平方得，cos²‎x+sin²‎x-2cos‎xsinx=18/25,
1-sin2x=18/25,sin2x=7/18

Answer 2

sin2x = sin [2(π/4+x) - π/2 ] = - cos 2(π/4+x) = 1 - 2 [ cos 2(π/4+x) ]^2 = 7/25

Answer 3

cos(π/2+2x)=2(cos(π/4+x))^2-1=-7/25
sin2π=-cos（π/2+2x）=7/25

Answer 4

-cos[2（π/4+x）]=-[2cos^2(π/4+x）-1]
sin2x=sin[2(π/4+x）-π/2]=-「2cos^2(π/4+x）-1]=7/25