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Math Help - Identity

  1. #1
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    Identity

    I am right to say that the identity of sec^2 is 1/sin^2
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  2. #2
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    Re: Identity

    Quote Originally Posted by Googl View Post
    I am right to say that the identity of sec^2 is 1/sin^2
    Do you mean \sec^{2}x=\frac{1}{\sin^{2}x} ? If so it is incorrect.

    The correct identity is,

    \sec{x}=\frac{1}{\cos{x}}\Rightarrow \sec^{2}x=\frac{1}{\cos^{2}x}
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  3. #3
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    Re: Identity

    Sorry, I meant that one. What I really wanted to find out is when the power changes the corresponding identity changes, so for example:

    sec^7x = 1/cos^2x
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  4. #4
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    Re: Identity

    Quote Originally Posted by Googl View Post
    Sorry, I meant that one. What I really wanted to find out is when the power changes the corresponding identity changes, so for example:

    sec^7x = 1/cos^2x
    Again what you have written is incorrect. I do not quite understand what you want to find out. Can you elaborate.

    \sec{x}=\frac{1}{\cos{x}}\Rightarrow \left(\sec x\right)^7=\left(\frac{1}{\cos x}\right)^7\Rightarrow \sec^{7}x=\frac{1}{\cos^{7}x}
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  5. #5
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    Re: Identity

    Quote Originally Posted by Googl View Post
    Sorry, I meant that one. What I really wanted to find out is when the power changes the corresponding identity changes, so for example:

    sec^7x = 1/cos^2x
    The above statement is not an identity because the quantities you wrote on each side of the = are not the same.


    sec^{7}x =  \frac{1}{cos^{2}x}


    which would be the same as writing down


     \left (\frac{1}{cos(x)}  \right ) ^{7}  =   \left ( \frac{1}{cos(x)} \right )^{2}

    which is incorrect

    If you have the proper identity


    sec(x) = \frac{1}{cos}


    both sides need to be raised to the same power to maintain the identity.
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  6. #6
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    Re: Identity

    Yes, the statement is wrong. Bad keyboard. I found the answer to what I was after.

    Thanks for the help.
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