Verify sin2X=(2tanX)/(1+tan^2X)

Question

I need to verify this for homework and im confused

Answer 1

2tanx / (1+tan²x) = 2tanx / sec²x

 

                           = (2sinx/cosx) / (1/cos²x)

 

                            = (2sinx/cosx)(cos²x/1)  = 2sinxcosx = sin(2x)

 

 

Answer 2

(2tanX)/(1+tan^2X)=

 

= 2/[1/tan(x)=tan(x)]=

 

= 2/[(sin²(x}+cos²(x))/(sin(x)cos(x))]=

 

= 2/[1/(sin(x)cos(x))]= 2(sin(x)cos(x)=sin(2x)