Posted by **help me out it's urgent** on Saturday, October 6, 2012 at 12:20pm.

show that cos2x=1-tan^ 2 x /1+tan^2x=2cos^2x-1

- trignometry -
**Reiny**, Saturday, October 6, 2012 at 12:45pm
cos 2x

= cos(x+x)

= cosxcosx - sinxsinx

= cos^2 x - sin^2 x

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

= 2 cos^2 x - 1, the last part of your equation.

all we need it to look at now is the middle part of

(1 - tan^2 x)/(1 + tan^2 x) , notice the necessary brackets

= (1 - sin^2 x/cos^2 x)/(1 + sin^2 x/cos^2 x)

= [ (cos^2 x - sin^2 x)/cos^2 x ]/[ (cos^2 x + sin^2 x)/cos^2 x ]

= (cos^2 x - sin^2 x)/cos^2 x * cos^2 x/(cos^2 x + sin^2 x)

= (cos^2 x - sin^2 x)/1

= cos^2 x - sin^2 x

as seen above

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