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Thread: Prove the equation

  1. #1
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    Prove the equation

    sin2x+cos2x=1
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  2. #2
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    Re: Prove the equation

    Have you attempted a web search on the topic?

    Prove the Pythagorean identity
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  3. #3
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    Re: Prove the equation

    Just draw a right triangle. Select and angle
    fine sine and cosine of the selected angle in terms of sides.
    Substitute the values in Left hand side of the equation and simplify
    Keep in mind the Pythagoras Theorem
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  4. #4
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    Re: Prove the equation

    $\sin\,x=\dfrac{opposite}{hypotenuse}$

    $\sin^2\,x= \left( \dfrac{opposite}{hypotenuse} \right)^2$

    $\cos\,x=\dfrac{adjacent}{hypotenuse}$

    $\cos^2\,x= \left (\dfrac{adjacent}{hypotenuse} \right)^2$

    $\sin\,x+\cos^2\,x= \left (\dfrac{opposite}{hypotenuse} \right)^2+ \left (\dfrac{adjacent}{hypotenuse} \right)^2$

    $= \left (\dfrac{(opposite)^2+(adjacent )^2}{(hypotenuse)^2} \right)$

    $=\dfrac{(hypotenuse)^2}{(hypotenuse)^2}$

    $=1$
    Last edited by deesuwalka; Nov 29th 2016 at 10:28 PM.
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  5. #5
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    Re: Prove the equation

    There exist a number of different ways to prove that. How you prove it depends strongly on how you are defining sine and cosine- which of the many definitions of sine and cosine are you using?
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