• Feb 8th 2006, 01:27 PM
aussiekid90
Hello, I have had quite a bit of troule with three of the trig problems that i had for homework. If you could show me the steps to get the answer that would be great because i'm sure there's going to be a problem like these on a quiz we will have pretty soon.

1. sec(x)+csc(x)
-------------- Express in 1 trig function
1+(tan(x))

2. cos(x)
----------- + tan(x) Express in 1 trig function
1+sin(x)

3. (sin(x))(cox(x)+sin(x)tan(x))

Thanks ALOT for the help
• Feb 8th 2006, 01:52 PM
CaptainBlack
Quote:

Originally Posted by aussiekid90

1. sec(x)+csc(x)
-------------- Express in 1 trig function
1+(tan(x))

$\frac{\sec(x)+\csc(x)}{1+\tan(x)}=\frac{1/\cos(x)+1/\sin(x)}{1+\tan(x)}=$ $\frac{\sin(x)+\cos(x)}{\cos(x) \sin(x)}\ \frac{1}{1+\tan(x)}=\frac{\sin(x)+\cos(x)}{\sin(x) [\cos(x)+\sin(x)]}=\csc(x)$

RonL
• Feb 8th 2006, 02:01 PM
CaptainBlack
Quote:

Originally Posted by aussiekid90
2. cos(x)
----------- + tan(x) Express in 1 trig function
1+sin(x)

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

RonL
• Feb 8th 2006, 02:12 PM
CaptainBlack
Quote:

Originally Posted by aussiekid90

3. (sin(x))(cox(x)+sin(x)tan(x))

$\sin(x) (\cos(x) + \sin(x) \tan(x))=\sin(x) \cos(x) + \sin ^2(x) \tan(x)$ $=\sin(x) \cos(x) + \frac{\sin ^3(x)}{ \cos(x)}=\frac{\sin(x) \cos^2(x)+\sin^3(x)}{\cos(x)}$

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

RonL