Question

已知sin(2a+x)=2sinx.求证：tan(a+x)=3tana

Answer 1

因为

sin(2a+x) = sin(a+x+a) = sin(a+x)cos(a)+cos(a+x)sin(a)

2sin(x) = 2sin(a+x-a) = 2sin(a+x)cos(a)-2cos(a+x)sin(a)

sin(2a+x)=2sin(x)

所以整理可得

sin(a+x)cos(a) = 3cos(a+x)sin(a)

即

sin(a+x)/cos(a+x) = 3 sin(a)/cos(a)

可证

tan(a+x) = 3 tan(a)