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Find the exact value of

1. tan 75 degrees
2. Cos 15 degrees
3. Sin 105 degrees

  • math -

    you know the values for 30 and 45 degrees
    use your sum/difference and half-angle formulas

    75=45+30
    15=30/2
    105=90+15

  • math -

    Tan 75 = tan (45 +30)
    = tan 45 + tan 30/1-tan 45 *tan 30
    = (1+ 1/√3)/(1-1/√3) = √3 + 1/√3-1
    = √3 + 1/√3-1 (afterationalization )
    = 2+√3
    cos 15 = cos (45 - 30)

    = cos 45 cos 30+ sin 45 sin 30
    =

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