# Thread: Need help in solving trigo an

1. ## [Solved] Need help in solving trigo an

Given that tan(2A) = (2tanA)/(1-tan^2 A)

show that tan(22.5) = sqrt(2) - 1

2. ## 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?

3. ## Re: Need help in solving trigo an

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

4. ## 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...

5. ## Re: Need help in solving trigo an

Ohhhh! I'm im able to solve it now!!! THANKS THANKS THANKS!!!