
Verify identity
am terrible with identity and this book proposes no answers or how to for the HW.
I can do the examples given okay but when it comes to the homework it's like wtf is all this. The problem is:
(sin@+cos@)^2=1+sin2@
i need to verify that one side equals the other.
only thing i know is that sin2@=2sin@cos@.

The two sides do NOT equal each other.
$\displaystyle \sin^2{\theta} + \cos^2{\theta} \equiv 1$ is a well known Identity known as the Pythagorean Identity.
Since $\displaystyle \sin{2\theta}$ is NOT identically equal to $\displaystyle 0$, (though it does equal $\displaystyle 0$ for CERTAIN values of $\displaystyle \theta$).
That means that the LHS can not possibly equal the RHS for ALL $\displaystyle \theta$.

sorry i wrote the problem wrong! I started this a day ago and i typed it from my page not the book.
It's (sin@+cos@)^2=1+sin2@

$\displaystyle (\sin{\theta} + \cos{\theta})^2 = \sin^2{\theta} + 2\sin{\theta}\cos{\theta} + \cos^2{\theta}$
$\displaystyle = \sin^2{\theta} + \cos^2{\theta} + 2\sin{\theta}\cos{\theta}$
$\displaystyle = 1 + 2\sin{\theta}\cos{\theta}$
$\displaystyle = 1 + \sin{2\theta}$.

Can i get help with this other one?
sin2ttant=tantcost2t
2sintcostsint/cost
(2sintcost^2/cost)  (sint/cost)
(2sintcost^2  sint)/cost

$\displaystyle \frac{2sintcos^2t  sint}{cost}$
= $\displaystyle \frac{sint(2cos^2t  1)}{cost}$
= tant cos2t

thanks guys, that helped me solving these annoying problems, i'm understanding the more complex ones a little better now. I have an exam on Tuesday >_< gotta keep studying.