Perform Addition and simplify trigonometric expression

I have the following problem... (Headbang)

$\displaystyle \frac{9 cos(x)}{1+sin(x)}+\frac{9+9sin(x)}{cos(x)}$

First get the same denominator

$\displaystyle \frac{cos(x) (9 cos(x))}{cos(x) (1+sin(x))}+ \frac{1+sin(x) (9+9sin(x))}{1+ sin(x) (cos(x))}$

Here its were I start to run into some confusion of distribution. I see the first fraction is correct but the second its not.. What am I doing wrong?

$\displaystyle \frac{9 cos^2(x)}{cos(x) (1+sin(x))}+ \frac{9 + 18sin(x)+9sin^2(x)}{cos(x) (1+sin(x))}$

Re: Perform Addition and simplify trigonometric expression

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**vaironxxrd** I have the following problem... (Headbang)

$\displaystyle \frac{9 cos(x)}{1+sin(x)}+\frac{9+9sin(x)}{cos(x)}$

First get the same denominator

$\displaystyle \frac{cos(x) (9 cos(x))}{cos(x) (1+sin(x))}+ \frac{1+sin(x) (9+9sin(x))}{1+ sin(x) (cos(x))}$

Here its were I start to run into some confusion of distribution. I see the first fraction is correct but the second its not.. What am I doing wrong?

$\displaystyle \frac{9 cos^2(x)}{cos(x) (1+sin(x))}+ \frac{9 + 18sin(x)+9sin^2(x)}{cos(x) (1+sin(x))}$

First of all, you MUST use brackets where they are needed. Please review what you have written. However, I can see your thought process and what you have ended up with is a correct answer. Why do you think it's incorrect?

Re: Perform Addition and simplify trigonometric expression

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**Prove It** First of all, you MUST use brackets where they are needed. Please review what you have written. However, I can see your thought process and what you have ended up with is a correct answer. Why do you think it's incorrect?

Did I overuse them, or did I just not place them in the right position?

Maybe I'm not trying hard enough, I'll give it a couple more tries.

Re: Perform Addition and simplify trigonometric expression

In the second fraction, the [1 + sin(x)] in the numerator and denominator needs to be in brackets, because you are multiplying the top and bottom by that entire expression.

Re: Perform Addition and simplify trigonometric expression

Oh i see.... Order of operations

$\displaystyle \frac{9 cos^2(x)}{cos(x) (1+sin(x))}+ \frac{9 + 18sin(x)+9sin^2(x)}{cos(x) (1+sin(x))}$ =

$\displaystyle \frac{9 cos^2(x) + 9 sin^2(x)+ 18sin(x) + 9}{cos(x) (1+sin(x))}$ =

$\displaystyle \frac{10 + 18sin(x) }{cos(x) (1+sin(x))}$ =

$\displaystyle \frac{10 + 18 }{cos(x) \cdot 1}$ =

$\displaystyle \frac{28}{cos(x) \cdot 1}$ =

$\displaystyle 28\cdot sec(x)$

Re: Perform Addition and simplify trigonometric expression

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**vaironxxrd** Oh i see.... Order of operations

$\displaystyle \frac{9 cos^2(x)}{cos(x) (1+sin(x))}+ \frac{9 + 18sin(x)+9sin^2(x)}{cos(x) (1+sin(x))}$ =

$\displaystyle \frac{9 cos^2(x) + 9 sin^2(x)+ 18sin(x) + 9}{cos(x) (1+sin(x))}$ =

$\displaystyle \frac{10 + 18sin(x) }{cos(x) (1+sin(x))}$

Correct up to here. But you can not cancel off any sin(x) values because your factor on the bottom is not sin(x), it's [ 1 + sin(x) ]. This is the furthest you can go.

Re: Perform Addition and simplify trigonometric expression

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**Prove It** Correct up to here. But you can not cancel off any sin(x) values because your factor on the bottom is not sin(x), it's [ 1 + sin(x) ]. This is the furthest you can go.

Oh so that's another reason for the brackets

Re: Perform Addition and simplify trigonometric expression

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**Prove It** Correct up to here. But you can not cancel off any sin(x) values because your factor on the bottom is not sin(x), it's [ 1 + sin(x) ]. This is the furthest you can go.

Actually when I use the calculator this equation is not equal. I don't mean to nag you about this, but I'm really trying different options and none of my answers work.

Re: Perform Addition and simplify trigonometric expression

I expect that they ARE equal, they just don't look it. There are many equivalent ways to write a trigonometric expression. What have you been told the "right" answer is?

Re: Perform Addition and simplify trigonometric expression

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**Prove It** I expect that they ARE equal, they just don't look it. There are many equivalent ways to write a trigonometric expression. What have you been told the "right" answer is?

It's an online course I'm redoing a homework I din't get 100% on and It's telling me, $\displaystyle \frac{10+18sin(x)}{cos(x)[1+sin(x)]}$ its not the right answer.

Re: Perform Addition and simplify trigonometric expression

Then you'll have to speak to your lecturer, as the answer is definitely correct.

Re: Perform Addition and simplify trigonometric expression

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**Prove It** Then you'll have to speak to your lecturer, as the answer is definitely correct.

I got help and solved it.

= $\displaystyle \frac{9[cos^2(x)+sin^2(x)] + 9 + 18sin(x)}{cos(x)[1+sin(x)]}$ =

$\displaystyle \frac{18+18 sin(x))}{cos(x)[1+sin(x)]}$ =

$\displaystyle \frac{18[1+sin(x)]}{cos(x)[1+sin(x)]}$ =

$\displaystyle 18sec(x)$

Re: Perform Addition and simplify trigonometric expression

It is well known my arithmetic is shocking, how could I think 9 + 9 = 10? Hahaha. Glad you finished it.