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Math Help - Perform Addition and simplify trigonometric expression

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    Senior Member vaironxxrd's Avatar
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    Perform Addition and simplify trigonometric expression

    I have the following problem...

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

    First get the same denominator

    \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?

    \frac{9 cos^2(x)}{cos(x) (1+sin(x))}+ \frac{9 + 18sin(x)+9sin^2(x)}{cos(x) (1+sin(x))}
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by vaironxxrd View Post
    I have the following problem...

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

    First get the same denominator

    \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?

    \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?
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    Senior Member vaironxxrd's Avatar
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by Prove It View Post
    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.
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    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.
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    Re: Perform Addition and simplify trigonometric expression

    Oh i see.... Order of operations

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

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

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

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

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

    28\cdot sec(x)
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by vaironxxrd View Post
    Oh i see.... Order of operations

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

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

    \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.
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by Prove It View Post
    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
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by Prove It View Post
    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.
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    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?
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by Prove It View Post
    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, \frac{10+18sin(x)}{cos(x)[1+sin(x)]} its not the right answer.
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    Re: Perform Addition and simplify trigonometric expression

    Then you'll have to speak to your lecturer, as the answer is definitely correct.
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    Re: Perform Addition and simplify trigonometric expression

    Quote Originally Posted by Prove It View Post
    Then you'll have to speak to your lecturer, as the answer is definitely correct.
    I got help and solved it.

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

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

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

    18sec(x)
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    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.
    Thanks from vaironxxrd
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