# Thread: Help needed on trigonometric proofs

1. ## 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

2. 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

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

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