# Adding and simplifying trigonometric expression

• Mar 17th 2013, 05:48 PM
vaironxxrd
Adding and simplifying trigonometric expression
I keep having problem with simplification problems...

My problem is: $\displaystyle \frac{6tan(x)}{1+sec(x)}+\frac{6+6sec(x)}{tan(x)}$

The answer given is: $\displaystyle 12csc(x)$ but I cannot reach this answer.

My attempt is...

$\displaystyle \frac{6tan^2(x)}{tan(x)[1+sec(x)]}+\frac{[1+sec(x)](6+6sec(x))}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6tan^2(x)}{tan(x)[1+sec(x)]}+\frac{6+12sec(x)+6sec^2(x)}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6tan^2(x) +6sec^2(x) + 12sec(x)+ 6}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6(tan^2(x) +sec^2(x) + 2sec(x)+ 1)}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6(tan^2(x) +sec^2(x) + 2sec(x)+ 1)}{tan(x)[1+sec(x)]}$ =

$\displaystyle \frac{6(2sec^2(x) + 2sec(x))}{tan(x)[1+sec(x)]}$
• Mar 17th 2013, 06:01 PM
zhandele
Re: Adding and simplifying trigonometric expression
You're very close. Just keep going a little further. See the pdf.
• Mar 17th 2013, 06:12 PM
vaironxxrd
Re: Adding and simplifying trigonometric expression
Quote:

Originally Posted by zhandele
You're very close. Just keep going a little further. See the pdf.

Thanks for that detailed set of instructions, I can't understand why can I not complete some simple simplification.
• Mar 17th 2013, 06:17 PM
zhandele
Re: Adding and simplifying trigonometric expression
Your work was quite accurate. Maybe you just got tired near the end. Don't worry about it, it'll be easier next time.