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TRIG/ALGEBRA

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1) Find the exact value. Use a sum or difference identity.
tan (-15 degrees)


2) Rewrite the following expression as a trigonometric function of a single angle measure.

cos 3x cos 4x - sin 3x sine 4x

  • TRIG/ALGEBRA -

    1.
    tan 15 = tan(45-30)
    = (tan45-tan30)/(1 + tan45tan30)
    = (1 - 1/√3)/(1 + 1/√3)
    multiply by √3/√3
    = (√3-1)/(√3+1)
    but tan(-15) = -tan15
    so
    tan(-15°) = (1-√3)/(√3 + 1)


    cos 3x cos 4x - sin 3x sine 4x
    = cos(3x+4x) = cos 7x

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