Prove: tan2x=2cos^(2)x/cot(x)-sin(2x)

Question

need help please thanks 

Answer 1

 

Hi,

 

Prove tan 2x = 2 tanx/(1-tan²x)

 

There are nearly always more than one path to a trig proof. This works but I don't know if it's the shortest

 

tan 2x = 2tan x/(1 - tan²x)

 

  =(2sinx/cosx)/(1-sin²x/cos²x)        Now multiply by cos²x

 

  = 2sinxcosx/(cos²x - sin²x)            substitute (1-sin²x) for the cos²x

 

  = 2sinxcosx/(1 - sin²x - sin²x)

 

=  2sinxcosx/(1 - 2sin²x)                 divide by sinx

 

= 2cosx/(1/sinx -2sinx)                    multiply by cosx

 

  = 2cos²x/(cosx/sinx -2sinxcosx)       remember sin2x = 2sinxcosx

 

  = 2cos²x/(cotx - sin2x)

 

 

 

 

 

 

 

 

tan2x=2cos^(2)x/cot(x)-sin(2x)