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Math Help - Verify trig identity

  1. #1
    Junior Member
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    Verify trig identity

    verify the identity.

    cos(pi-theta) + sin(pi/2 + theta) = 0



    can anyone please explain... Thanks!!!
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  2. #2
    Super Member

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    Hello, overduex!

    One method is to use the Compound-angle Formulas:

    . . \sin(A + B) \;=\;\sin(A)\cos(B) + \sin(B)\cos(A)

    . . \cos(A - B) \;=\;\cos(A)\cos(B) + \sin(A)\sin(B)


    Verify the identity: . <br />
\cos(\pi-\theta) + \sin\left(\frac{\pi}{2}  + \theta\right) \;= \;0

    Using the two formulas, we have:

    . . ,. . \cos(\pi)\cos\theta + \sin(\pi)\sin\theta + \sin\frac{\pi}{2}\cos\theta + \sin\theta\cos\frac{\pi}{2}

    . . = \;\;-1\cdot\cos\theta + 0\cdot\sin\theta + 1\cdot\cos\theta + \sin\theta\cdot0 \;\;=\;\;-\cos\theta + 0 + \cos\theta + 0 \;=\;0

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