Identity conundrum

**nightrider456** · May 31st 2010, 07:50 PM

Having troubles proving the identity
tanx/secx+1 = 2cosx-2cosx^2x/sin2x
Thanks

**pickslides** · May 31st 2010, 08:23 PM

What have you tried?

Does this help?

$\frac{\tan x}{\sec x+1}\times \frac{\sec x-1}{\sec x-1}= \frac{\tan x (\sec x-1)}{\sec^2 x-1}= \frac{\tan x (\sec x-1)}{\tan^2 x}$

**nightrider456** · May 31st 2010, 09:02 PM

still having troubles

**Isomorphism** · June 1st 2010, 02:58 AM

Now, does this help?

$\frac{\tan x (\sec x-1)}{\tan^2 x} = \frac{\cos x(\sec x-1)}{\sin x} = \frac{2\cos^2 x(\sec x-1)}{2\cos x \sin x} = \frac{2\cos^2 x\sec x - 2\cos^2 x}{\sin 2x}$

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