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Thread: trig proof

  1. #1
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    trig proof

    In triangle ABC, angle C is 90 degrees. show that;

    $\displaystyle sin2A = \frac{2ab}{c^{2}} $

    $\displaystyle sin\frac{1}{2}A = \sqrt{\frac{c-b}{2c}} $

    Can someone please explain what to do, as I dont understand the question very well.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Tweety View Post
    In triangle ABC, angle C is 90 degrees. show that;

    $\displaystyle sin2A = \frac{2ab}{c^{2}} $

    $\displaystyle sin\frac{1}{2}A = \sqrt{\frac{c-b}{2c}} $

    Can someone please explain what to do, as I dont understand the question very well.

    Thanks in advance.
    use the fact that $\displaystyle \sin(2A)=2\sin(A)\cos(A)$
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  3. #3
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    and remember,
    $\displaystyle \sin(A)=\frac {\textrm{opposite}} {\textrm{hypotenuse}} $
    $\displaystyle \cos(A)=\frac {\textrm{adjacent}} {\textrm{hypotenuse}} $
    it's up to you to see what is $\displaystyle a$,$\displaystyle b$ and $\displaystyle c$.
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  4. #4
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    Quote Originally Posted by Raoh View Post
    and remember,
    $\displaystyle \sin(A)=\frac {\textrm{opposite}} {\textrm{hypotenuse}} $
    $\displaystyle \cos(A)=\frac {\textrm{adjacent}} {\textrm{hypotenuse}} $
    it's up to you to see what is $\displaystyle a$,$\displaystyle b$ and $\displaystyle c$.

    Oh so the sides are a,b and c? So do I draw a right angled triangle and and label the hypotenuse c?
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  5. #5
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    Quote Originally Posted by Tweety View Post
    Oh so the sides are a,b and c? So do I draw a right angled triangle and and label the hypotenuse c?
    yes,the hypotenuse is c.
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