show question for trig. (1 Viewer)

[bossleymaths]

if t=tan x/2 , show that sinx=2t / 1+t^2

 

[tacogym27101990]

tanx= tan(x/2+x/2)
=(2tanx/2)/(1-tan²x/2)
=2t/1-t²
then just draw up a right angle triangle and find an expression for the hypotenuse

 

[tommykins]

if t=tan x/2 , show that sinx=2t / 1+t^2

sinx = 2sinx/2.cosx/2
= [2sinx/2.cosx/2]/sin²x+cos²x
= [2tanx/2]/1+tan²x/2 dividing everything by cos²x/2
= 2t/1+t²