1. ## Identity

I am right to say that the identity of sec^2 is 1/sin^2

2. ## Re: Identity

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

The correct identity is,

$\displaystyle \sec{x}=\frac{1}{\cos{x}}\Rightarrow \sec^{2}x=\frac{1}{\cos^{2}x}$

3. ## 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

4. ## Re: Identity

Originally Posted by Googl
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.

$\displaystyle \sec{x}=\frac{1}{\cos{x}}\Rightarrow \left(\sec x\right)^7=\left(\frac{1}{\cos x}\right)^7\Rightarrow \sec^{7}x=\frac{1}{\cos^{7}x}$

5. ## Re: Identity

Originally Posted by Googl
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.

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

which would be the same as writing down

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

which is incorrect

If you have the proper identity

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

both sides need to be raised to the same power to maintain the identity.

6. ## Re: Identity

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

Thanks for the help.