Identity

**Googl** · June 24th 2011, 09:42 PM

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

**Sudharaka** · June 24th 2011, 10:39 PM

Originally Posted by Googl

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,

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

**Googl** · June 24th 2011, 11:39 PM

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

**Sudharaka** · June 25th 2011, 12:59 AM

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.

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

**Tacos** · June 25th 2011, 10:26 AM

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.

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

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.

**Googl** · June 26th 2011, 08:30 AM

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

Thanks for the help.

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