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Math Help - [SOLVED] Verifying Trig identities

  1. #1
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    [SOLVED] Verifying Trig identities

    Umm the question is

    sin(3pi-x) = sinx

    well i figured to use the sum and difference formulas but after i change it to the formula i get stuck... and i dont know where elso to go

    same with these other ones-

    cos(5pi/4-x) = square root of -2/2(cos x + sin x)
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  2. #2
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    Hello, jamespk07!

    You're expected to know some standard trig values . . .


    Prove: . \sin(3\pi-x) \:= \:\sin x

    \sin(3\pi-x) \:=\:\sin(3\pi)\cos(x) - \sin(x)\cos(3\pi)

    . . . . . . . = \;0\cdot\cos(x) - \sin(x) \cdot(-1)

    . . . . . . . = \;\sin x




    \cos\left(\tfrac{5\pi}{4}-x\right) \:=\:\text{-}\tfrac{\sqrt{2}}{2}(\cos x + \sin x)

    \cos\left(\tfrac{5\pi}{4} - x\right) \;=\;\cos\left(\tfrac{5\pi}{4}\right)\cos x - \sin\left(\tfrac{5\pi}{4}\right)\sin x

    . . . . . . . . = \;\left(\text{-}\tfrac{\sqrt{2}}{2}\right)\cos x + \left(\text{-}\tfrac{\sqrt{2}}{2}\right)\sin x

    . . . . . . . . = \;\text{-}\tfrac{\sqrt{2}}{2}(\cos x + \sin x)

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