# Thread: Help with trig identity proofs

1. ## Help with trig identity proofs

Hi,
I'm looking for help with two trig proof/verify problems. They are:

1. SINX + COSX . COTX = CSCX

2. ((1 + COSX) / SINX) + (SINX/ (1 + COSX)) = 2CSCX

Mike Clemmons

2. Originally Posted by Mike Clemmons
Hi,
I'm looking for help with two trig proof/verify problems. They are:

1. SINX + COSX . COTX = CSCX

2. ((1 + COSX) / SINX) + (SINX/ (1 + COSX)) = 2CSCX

Mike Clemmons
1. $\sin{x} + \cos{x}\cot{x} = \sin{x} + \cos{x}\left(\frac{\cos{x}}{\sin{x}}\right)$

$= \frac{\sin^2{x}}{\sin{x}} + \frac{\cos^2{x}}{\sin{x}}$

$= \frac{\sin^2{x} + \cos^2{x}}{\sin{x}}$

$= \frac{1}{\sin{x}}$

$= \csc{x}$.

3. Originally Posted by Mike Clemmons
Hi,
I'm looking for help with two trig proof/verify problems. They are:

1. SINX + COSX . COTX = CSCX

2. ((1 + COSX) / SINX) + (SINX/ (1 + COSX)) = 2CSCX

Mike Clemmons
2. $\frac{1 + \cos{x}}{\sin{x}} + \frac{\sin{x}}{1 + \cos{x}}$

$= \frac{(1 + \cos{x})(1 + \cos{x})}{\sin{x}(1 + \cos{x})} + \frac{\sin{x}\sin{x}}{\sin{x}(1 + \cos{x})}$

$= \frac{(1 + \cos{x})^2 + \sin^2{x}}{\sin{x}(1 + \cos{x})}$

$= \frac{1 + 2\cos{x} + \cos^2{x} + \sin^2{x}}{\sin{x}(1 + \cos{x})}$

$= \frac{1 + 2\cos{x} + 1}{\sin{x}(1 + \cos{x})}$

$= \frac{2 + 2\cos{x}}{\sin{x}(1 + \cos{x})}$

$= \frac{2(1 + \cos{x})}{\sin{x}(1 + \cos{x})}$

$= \frac{2}{\sin{x}}$

$= 2\csc{x}$.

4. Prove it,
Thanks very much..... On a different tack, we live in North Carolina, but lived in Manly NSW for about 3 years in the 80s. Loved every minute of it.
Mike Clemmons

5. Originally Posted by Mike Clemmons
Prove it,
Thanks very much..... On a different tack, we live in North Carolina, but lived in Manly NSW for about 3 years in the 80s. Loved every minute of it.
Mike Clemmons
I enjoyed Manly when I went there a few years ago. Awesome beach!