Need help in solving trigo an

• Sep 22nd 2012, 10:37 PM
ZGOON
[Solved] Need help in solving trigo an
Given that tan(2A) = (2tanA)/(1-tan^2 A)

show that tan(22.5) = sqrt(2) - 1
• Sep 22nd 2012, 11:03 PM
MarkFL
Re: Need help in solving trigo an
Define $A\equiv22.5^{\circ}$ and write the given double angle identity for tangent as:

$\tan(2(22.5^{\circ}))=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}$

$\tan(45^{\circ})=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}$

$1=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}$

Can you finish?
• Sep 22nd 2012, 11:09 PM
ZGOON
Re: Need help in solving trigo an
Quote:

Originally Posted by MarkFL2
Define $A\equiv22.5^{\circ}$ and write the given double angle identity for tangent as:

$\tan(2(22.5^{\circ}))=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}$

$\tan(45^{\circ})=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}$

$1=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}$

Can you finish?

I managed to get that part...
and i let tan(22.5) be Y
it becomes eqn [y^2 + 2y - 1 = 0]
but somehow i cant get the sqrt(2)

*im using the cross multiply method to solve the eqn
• Sep 22nd 2012, 11:14 PM
MarkFL
Re: Need help in solving trigo an
You have the correct quadratic...now either complete the square or use the quadratic formula.

You will get 2 roots. You will need to decide which is extraneous, either by substituting the roots into the original equation, or some knowledge of which quadrant the angle is in and what sign tangent has there...
• Sep 23rd 2012, 12:11 AM
ZGOON
Re: Need help in solving trigo an
Ohhhh! I'm im able to solve it now!!! THANKS THANKS THANKS!!!