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dy/dx[tan(y)=x=y] in terms of y

the answer my teacher got was cot^2(y) but i get is 1/[sec^2(y)-1]

either i made a mistake, my teacher made a mistake or we're both right and i just need to simplify.

please tell me which of the following is the case and how to get to the correct answer.

  • Calculus -

    let's see if cot^2 y = 1/(sec^2 y - 1 )

    RS = 1/(1/cos^2y - 1)
    = 1/((1 - cos^2y)/cos^2y)
    = 1/((sin^2y/cos^2))
    = cos^2y/sin^2y
    = cot^2 y

    so you are both right!

  • Calculus -

    ok, thank you. is it preferable to change it like that? cause i honestly have no idea why it would matter.

  • Calculus -

    oh and just to be clear you got this using trig identities right?

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