calculus

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Verify the identity

cot2 beta/1+csc beta=1-sin beta/sin beta.

  • calculus -

    did you mean
    cot^2 ß/(1+cscß) = (1-sinß)/sinß ?

    from the identity
    sin^ Ø + cos^2 Ø = 1
    if we divide each term by sin^2Ø ......
    1 + cot^2 Ø = csc^2 Ø ----> cot^2 Ø = csc^2Ø - 1

    LS
    = (csc^2 ß - 1)/(1 + csc ß)
    = (cscß + 1)(cscß - 1)/(1 + cscß)
    = cscß - 1
    = 1/sinß - sinß/sinß
    = (1 - sinß)/sinß
    = RS

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