Half angle or double angle Identities

**hellojellojw** · July 21st 2009, 12:36 PM

I don't understand them at all.
The problem is to evaluate tan(22.5) using exact values.
How should I do this?

**Krizalid** · July 21st 2009, 12:47 PM

$\tan \frac{x}{2}=\frac{\sin \frac{x}{2}}{\cos \frac{x}{2}}=\frac{\sqrt{\frac{1-\cos x}{2}}}{\sqrt{\frac{1+\cos x}{2}}}=\sqrt{\frac{1-\cos x}{1+\cos x}}.$

Actually is $\sin \frac{x}{2}=\pm \sqrt{\frac{1-\cos x}{2}},$ but the angle is positive, hence our answer is positive, and that's preserves the positive sign.

**hellojellojw** · July 21st 2009, 01:10 PM

Originally Posted by Krizalid

$\tan \frac{x}{2}=\frac{\sin \frac{x}{2}}{\cos \frac{x}{2}}=\frac{\sqrt{\frac{1-\cos x}{2}}}{\sqrt{\frac{1+\cos x}{2}}}=\sqrt{\frac{1-\cos x}{1+\cos x}}.$

Actually is $\sin \frac{x}{2}=\pm \sqrt{\frac{1-\cos x}{2}},$ but the angle is positive, hence our answer is positive, and that's preserves the positive sign.

hmm can I assume tan (22.5) is equal to tan 1/2 x?

**pickslides** · July 21st 2009, 01:52 PM

Krizalid is suggesting $x = \frac{\pi}{4}$

**hellojellojw** · July 21st 2009, 05:20 PM

Well, that was easier than I expected. Thanks.

Thread: Half angle or double angle Identities

LinkBack

Thread Tools

Display

Half angle or double angle Identities

Similar Math Help Forum Discussions

Double and half angle identities?

Simplify the Expression (Double-Angle or Half-Angle)

More double angle and Half angle problems

Help with double angle and half angle formulas

Double and Half angle identities

Search Tags