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Simplify (sin^2)*(67.5deg) - (cos^2)*(67.5deg) and then evaluate exactly.

  • Trig -

    well, cos 2x = cos^2 x - sin^2 x, so what do you think?

    If you end up with 1/√2 you are correct.

  • Trig -

    How exactly do you get there though? I tried to follow a similar homework problem and got:

    = (cos^2)*(67.5deg) - (sin^2)*(67.5deg)
    = cos(2*67.5deg)
    = cos135deg
    = -√2/2

  • Trig -

    note that the problem was

    = -cos(135)

    my hint was not intended to make you forget what was originally asked. :-)

    And, I know lots of folks hate roots in the denominator, but I see no reason why √2/2 is better than 1/√2. Just mt preference

  • Trig -

    Thank you very much!

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