How do you prove (sin 2x) / (1 + cos2x) = tan x?

1 Answer
Mar 20, 2016

see explanation

Explanation:

Manipulating the left side usingcolor(blue)" Double angle formulae "

• sin2x = 2sinxcosx

• cos2x = cos^2x - sin^2x

and using sin^2x + cos^2x = 1 " we can also obtain "

cos2x = (1 - sin^2x) - sin^2x = 1 - 2sin^2x

and cos2x = cos^2x - (1 - cos^2x ) = 2cos^2x - 1

rArr(sin2x)/(1+cos2x) = (2sinxcosx)/(1+2cos^2x-1) = (2sinxcosx)/(2cos^2x)

= (cancel(2) sinx cancel(cosx))/(cancel(2) cancel(cosx) cosx)= (sinx)/(cosx) = tanx = " right side "