# Find all solutions

• Mar 9th 2010, 06:28 PM
purplec16
Find all solutions
How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
$cos\theta=\frac{1}{sec\theta}$

$cos\theta sec\theta=1$

Is this right so far?, what is my next step
• Mar 9th 2010, 06:54 PM
Prove It
Quote:

Originally Posted by purplec16
How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
$cos\theta=\frac{1}{sec\theta}$

$cos\theta sec\theta=1$

Is this right so far?, what is my next step

This is not an equality that you can solve for $\theta$ with. It's an identity.

In other words

$\cos{\theta} = \frac{1}{\sec{\theta}}$ for ALL $\theta$, provided that the denominator does not equal $0$.
• Mar 9th 2010, 07:15 PM
purplec16
I still dont get it so I have to solve it first then find the solutions?
• Mar 9th 2010, 07:32 PM
Prove It

ANY number $\theta$ will satisfy this equation because IT IS AN IDENTITY. (as long as the number $\theta$ doesn't make the denominator $= 0$.)
• Mar 10th 2010, 01:37 AM
Quote:

Originally Posted by purplec16
How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
$cos\theta=\frac{1}{sec\theta}$

$cos\theta sec\theta=1$

Is this right so far?, what is my next step

Hi purplec16,

$\frac{1}{cos\theta}$ is $sec\theta$

"They" are equal for all $\theta$
as they are one and the same.

As $cos\theta$ ranges from -1 to 1 $sec\theta$ is never zero.
• Mar 10th 2010, 07:15 AM
purplec16
I thought the range of cos is 0 to 2pi?
• Mar 10th 2010, 09:34 AM
Hi purplec16,

the angle $\theta$ ranges from 0 to $2{\pi}$ over one period

and $Cos\theta$ ranges from -1 to 1