# Simplify the expression

• Feb 24th 2008, 05:44 PM
OzzMan
Simplify the expression
Simplify the given expression. The result will be one of $\displaystyle sin\; x, \;cos\; x,\; tan\; x,\; cot\; x,\; sec\; x,\; or\; csc\; x.$

$\displaystyle \frac{Tan\;x\;+\;Cot\;x}{Csc\;x}$

The answer to this one is $\displaystyle Sec\;x.$ I'm kinda confused on how they got it because I ended up with $\displaystyle Cos\;x$
• Feb 24th 2008, 05:51 PM
Jhevon
Quote:

Originally Posted by OzzMan
Simplify the given expression. The result will be one of $\displaystyle sin\; x, \;cos\; x,\; tan\; x,\; cot\; x,\; sec\; x,\; or\; csc\; x.$

$\displaystyle \frac{Tan\;x\;+\;Cot\;x}{Csc\;x}$

The answer to this one is $\displaystyle Sec\;x.$ I'm kinda confused on how they got it because I ended up with $\displaystyle Cos\;x$

Note: $\displaystyle \frac {\tan x + \cot x}{\csc x} = \sin x (\tan x + cot x)$

csc(x) = 1/sin(x)

i suppose you did something like csc(x) = 1/cos(x). happens all the time
• Feb 24th 2008, 06:28 PM
OzzMan
Could you help me out with simplifying it? I'm kinda stuck. Can't seem to get Sec x as my answer.
• Feb 24th 2008, 06:38 PM
Jhevon
Quote:

Originally Posted by OzzMan
Could you help me out with simplifying it? I'm kinda stuck. Can't seem to get Sec x as my answer.

$\displaystyle \sin x (\tan x + \cot x) = \sin x \tan x + \sin x \cot x = \sin x \cdot \frac {\sin x}{\cos x} + \sin x \cdot \frac {\cos x}{\sin x}$

now simplify the fractions, combine them and continue
• Feb 24th 2008, 06:50 PM
OzzMan
Thanks. Very long problem, but I got the right answer. (Rofl)