# Help needed on trigonometric proofs

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• May 3rd 2009, 09:33 AM
bkstudent14
Help needed on trigonometric proofs
i was wondering if ANYONE could help me with some proofs i missed a couple days of trig. and im totally lost so here they are

1. 1-cos(2a)/sin(2a)=tana

2. cos(2a)= 1-tan^2a/1+tan^2a

3. tan(2a)= 2/cota-tana

thanks in advance
• May 3rd 2009, 10:01 AM
running-gag
Quote:

Originally Posted by bkstudent14
i was wondering if ANYONE could help me with some proofs i missed a couple days of trig. and im totally lost so here they are

1. 1-cos(2a)/sin(2a)=tana

Hi

$\frac{1-\cos(2a)}{\sin(2a)} = \frac{1-(1-2\sin^2a)}{2\sin a \cos a} = \frac{2\sin^2a}{2\sin a \cos a} = \tan a$

As usual my advice is
1) learn ans know perfectly the trig identities
2) practice a lot (Wink)
• May 3rd 2009, 10:30 AM
running-gag
Quote:

Originally Posted by bkstudent14
2. cos(2a)= 1-tan^2a/1+tan^2a

$\frac{1-\tan^2a}{1+\tan^2a} = \frac{1-\frac{\sin^2a}{\cos^2a}}{1+\frac{\sin^2a}{\cos^2a} } = \frac{\cos^2a-\sin^2a}{\cos^2a+\sin^2a} = \cos^2a-\sin^2a = \cos(2a)$