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Thread: Proof of an equation

  1. #1
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    Unhappy Proof of an equation

    Hello everyone!

    I'm new to this forum, I stumbled upon this domain because I really needed some help proving this equation. I'm generally horrible at this, even after practising for a bit and none of my friends are any better off than I am, so I couldn't get help anywhere.
    Anyway, I need step by step proof that sinēB + sinēC -sinēA = 2cosA * sinB * sinC
    If any of you could figure this out, that would be amazing.

    Thanks in advance

    SSG
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  2. #2
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    Re: Proof of an equation

    Quote Originally Posted by SillyStudentGuy View Post
    I'm new to this forum, I stumbled upon this domain because I really needed some help proving this equation. I'm generally horrible at this, even after practising for a bit and none of my friends are any better off than I am, so I couldn't get help anywhere. Anyway, I need step by step proof that sinēB + sinēC -sinēA = 2cosA * sinB * sinC
    Have you even tested these?
    Look at this sum. Then look Here.
    Are they equal?

    Have you stated the question corrected?
    Thanks from SillyStudentGuy
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  3. #3
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    Re: Proof of an equation

    Thank you very much for replying.

    I forgot to mention that A, B and C represent corners of a triangle. Upon testing, using 60° for A, 80° for B and 40°, I found that both sides were equal (0.63302222)

    SSG
    Last edited by SillyStudentGuy; Mar 4th 2018 at 01:51 PM.
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  4. #4
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    Re: Proof of an equation

    Quote Originally Posted by SillyStudentGuy;933537[COLOR="#FF0000"
    I forgot to mention that A, B and C represent corners of a triangle[/COLOR]. Upon testing, using 60° for A, 80° for B and 40°, I found that both sides were equal (0.63302222)
    Don't you think that is important? Now that is an identity. In fact at some point I worked out something similar. I am not spending the time again.

    Here are hint aids. $(A+B+C)=\pi$, $\sin(A+B+C)=\cos(B) \cos(C) \sin(A) + \cos(A) \cos(C) \sin(B) + \cos(A) \cos(B) \sin(C) - \sin(A) \sin(B) \sin(C)$ See Here.

    Because $\sin(X+Y)=\sin(X)\cos(Y)+\sin(Y)\cos(X)$ what does $\sin(\pi-A)=~?$

    Good luck!
    Last edited by Plato; Mar 4th 2018 at 03:49 PM.
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  5. #5
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    Re: Proof of an equation

    Quote Originally Posted by SillyStudentGuy View Post
    Hello everyone!

    I'm new to this forum, I stumbled upon this domain because I really needed some help proving this equation. I'm generally horrible at this, even after practising for a bit and none of my friends are any better off than I am, so I couldn't get help anywhere.
    Anyway, I need step by step proof that sinēB + sinēC -sinēA = 2cosA * sinB * sinC
    If any of you could figure this out, that would be amazing.

    Thanks in advance

    SSG
    The first thing I would do is notice that is $A= B= C= \frac{\pi}{2}$, the left hand side is 1+ 1- 1= 1 while the right hand side is 2(0)(1)(1)= 0. The two sides are not equal- what you are trying to prove is not true!
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  6. #6
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    Re: Proof of an equation

    Quote Originally Posted by HallsofIvy View Post
    The first thing I would do is notice that is $A= B= C= \frac{\pi}{2}$, the left hand side is 1+ 1- 1= 1 while the right hand side is 2(0)(1)(1)= 0. The two sides are not equal- what you are trying to prove is not true!
    Hi, Prof G Ivy did you read this whole thread before posting this? Here is the salient addition:
    Quote Originally Posted by SillyStudentGuy View Post
    I forgot to mention that A, B and C represent corners of a triangle.
    SillyStudentGuy clearly means by "corners of a triangle" the angles of a triangles. In which case your example does not apply. With that addendum the equation is an identity.
    Last edited by Plato; Mar 4th 2018 at 06:22 PM.
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  7. #7
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    Re: Proof of an equation

    searching the web I found 1/2*twelve solutions.
    Here is one that I liked

    $a^2=b^2+c^2-2 b c \cos A$

    $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$

    replace $a,b,c$ from the second equation into the first and simplify
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