1. ## Verifying Identites

Verify the following identity:

2sin^2x +cos2x
_______________. =cosx
secx

or

2 sine squared x plus cosine 2 x divided by secant x

Can anyone do this problem for me and go over the steps...I've been going at it for a while and can't solve this ish.......I've used so many reciprocal identities and pythagreon identites and I still can't figure it out.

Thanks!

2. Originally Posted by sabes
Verify the following identity:

2sin^2x +cos2x
_______________
secx

or

2 sine squared x plus cosine 2 x divided by secant x

Can anyone do this problem for me and go over the steps...I've been going at it for a while and can't solve this ish.......I've used so many reciprocal identities and pythagreon identites and I still can't figure it out.

Thanks!
what you posted is not an identity, it is a trigonometric expression.

an identity is an equation. so, something is missing or you misread the instructions on what to do with the expression.

3. oh crap. I left out the "=cosx" bit at the end!

I'm sorry...could you still help?

Thanks

I'm sorry if I wasted any of your time if you were confused. I feel like a dummy. Sorry

4. try this ...

change $\cos(2x)$ in the numerator to $\cos^2{x} - \sin^2{x}$ and combine like terms.

... see what happens.

5. [size=3]Hello, sabes!

Verify the following identity: . $\frac{2\sin^2\!x +\cos2x}{\sec x} \:=\:\cos x$

We're expected to know this identity: . $\cos2x \:=\:2\cos^2\!x-1$

So: . $\frac{2\sin^2\!x + \cos2x}{\sec x} \;=\;\frac{2\sin^2\!x + (2\cos^2\!x - 1)}{\sec x} \;=\;\frac{2\overbrace{(\sin^2\!x+\cos^2\!x)}^{\te xt{This is 1}} - 1}{\sec x}$

. . $= \;\;\frac{2-1}{\sec x} \;\;=\;\;\frac{1}{\sec x} \;\;=\;\;\cos x$

6. Oh snap!

Thanks a ton guys.

I need help with one more if ya don't mind:

(sinx+cosx)^2 =1+sin2x

Now I foiled the first half of the equation and got stuck here:

Sin^2x + 2sinxcosx + cos^2x =1+sin2x

7. Originally Posted by sabes
Oh snap!

Thanks a ton guys.

I need help with one more if ya don't mind:

(sinx+cosx)^2 =1+sin2x

Now I foiled the first half of the equation and got stuck here:

Sin^2x + 2sinxcosx + cos^2x =1+sin2x
look at the left side.

you are expected to know these two identities ...

$\sin^2{x} + \cos^2{x} = 1$

$2\sin{x}\cos{x} = \sin(2x)$