Yet another "Verify the trig identity" prob...HELP

• December 7th 2008, 07:39 AM
calvin_coolidge
Yet another "Verify the trig identity" prob...HELP
Verify the following identity by starting with the left hand side.

tan^2(x/2+pi/4)=1+sinx/1-sinx.....don't have a "pi" character, hopefully that was understandable. Not quite sure how to start this. Should I just use an addition formula?....or do I need to use a formula to lower the power on the tan^2....????...Loosin' my mind here....

Thanks for any help.

~CC
• December 7th 2008, 08:27 AM
Chop Suey
Using the identity $\tan^2{x} = \frac{1-\cos{2x}}{1+\cos{2x}}$ and $\cos{(A\pm B)}=\cos{A}\cos{B} \mp \sin{A}\sin{B}$, we can write the LHS as:

$\frac{1-\cos{(x+\frac{\pi}{2})}}{1+\cos{(x+\frac{\pi}{2})} } = \frac{1+\sin{x}}{1-\sin{x}}$
• December 8th 2008, 06:36 AM
calvin_coolidge
Thank you for the help Chop Suey!

~CC