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Math Help - Need help with solving trig equations and trig identities

  1. #1
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    Need help with solving trig equations and trig identities

    1) 1 + sinx = cosx where -180 < x < 180 (Provide the general and particular solutions)

    2) Prove

    (cosx/2 - sinx/2)^2 = 1 - sinx

    3) Prove

    sin2A = 1 - 2sin^2 (45 - A)
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  2. #2
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    Re: Need help with solving trig equations and trig identities

    2. expand and use cos^2+sin^2 = 1. Use sin2x = 2sinxcosx identity.
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  3. #3
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    Re: Need help with solving trig equations and trig identities

    Quote Originally Posted by portage View Post
    1) 1 + sinx = cosx where -180 < x < 180 (Provide the general and particular solutions)

    square both sides, change cos2x to 1 - sin2x, and solve the resulting quadratic in sinx ... don't forget to check for extraneous solutions


    2) Prove

    (cosx/2 - sinx/2)^2 = 1 - sinx

    square the left side, then use the Pythagorean identity and the double angle identity for sine


    3) Prove

    sin2A = 1 - 2sin^2 (45 - A)

    use the difference identity for sine to find sin(45-A) , square the result, then use the double angle identity for sine.
    ...
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