verify an identity

**pacman** · September 1st 2009, 12:11 AM

verify this identity: tan (45 + A) + tan (45 - A) = 2 sec (2A).

**Grandad** · September 1st 2009, 12:49 AM

Hello pacman

Originally Posted by pacman

verify this identity: tan (45 + A) + tan (45 - A) = 2 sec (2A).

$\tan(45+A)+\tan(45-A) = \frac{\tan45+\tan A}{1-\tan45\tan A}+\frac{\tan45-\tan A}{1+\tan45\tan A}$

$=\frac{1+\tan A}{1-\tan A}+\frac{1-\tan A}{1+\tan A}$

$=\frac{(1+\tan A)^2 +(1-\tan A)^2}{(1+\tan A)(1-\tan A)}$

$= \frac{2+2\tan^2A}{1-\tan^2A}$

$= \frac{2\cos^2A+2\sin^2A}{\cos^2A - \sin^2A}$

$=\frac{2}{\cos2A}$

$=2\sec2A$

Grandad

**pacman** · September 1st 2009, 07:02 AM

That's a clean sweep Grandad, Thanks!

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