Mathematics

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How can I evaluate the expression below without using calculator?
cos15*2sin15

Thank you!

  • Mathematics -

    you can use the sum and difference rules

    cos15 = cos (45-30) = cos45*cos30 + sin45*sin30

    sin15 = sin (45-30) = sin45*cos30 - cos45*sin30

    45 and 30 are the common trig values to know

  • Mathematics -

    I got sqrt6/4 - sqrt2/4 for sin15 and sqrt6/4 + sqrt2/4 for cos15. Is it right?
    And the answer would be 6radical3/4???
    Thank you!

  • Mathematics -

    Also, can you give me the exact formulas for the sum and difference rules (both sin and cos) without substituting any angles there? Thanks.

  • Mathematics -

    OR

    cos15*2sin15
    = 2(sin15)(cos15)
    = sin 30
    = 1/2

  • Mathematics -

    How did you do this, Reiny? I don't understand. How does 2(sin15)(cos15) equal sin30? Please help!
    Thanks.

  • Mathematics -

    the "half-angle" formula

    sin 2A = 2(sinA)(cosA)

    in this case A = 15º

    by the way, you can check on a calculator

    your (cos15)(2sin15) = .5 or 1/2

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