Trigonometry

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Simplify the expression using trig identities:
1. (sin4x - cos4x)/(sin2x -cos2x)

2. (sinx(cotx)+cosx)/(2cotx)

  • Trigonometry -

    1.
    I am sure you mean
    (sin^4 x - cos^4 x)/(sin^2 x - cos^2 x)
    = (sin^2 x + cos^2 x )((sin^2 x - cos^2 x)/(sin^2 x - cos^2 x)
    = (sin^2 x + cos^2 x)
    =1

    2.
    (sinx(cotx)+cosx)/(2cotx)
    = (sinx(cosx/sinx) + cosx)/(2cosx/sinx)
    = (cosx + cosx)(sinx/(2cosx)
    = 2cosx(sinx)/(2cosx)
    = sinx

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