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...

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

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

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

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

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

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

1 Attachment(s)

Re: Adding and simplifying trigonometric expression

You're very close. Just keep going a little further. See the pdf.

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.

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.