1. ## Identities

Verify that the left side = the right side

$(sin t+cos t)^2= 1+ sin 2 t$

$sin^2t + 2 sin t cos t+ cos^2 t = 1+ sin 2 t$

$1+ 2sintcost= 1+ sin2t$

I cant seem to solve the identity

2. sin 2 t cos t
This should be
2sint cos t

3. Originally Posted by sa-ri-ga-ma
sin 2 t cos t
This should be
2sint cos t
I changed that, it was a typo

4. Originally Posted by sa-ri-ga-ma
sin 2 t cos t
This should be
2sint cos t
Do you know how to solve it from there?

5. Originally Posted by purplec16
Do you know how to solve it from there?
$\sin(2t) = 2\sin{t}\cos{t}$ is the well known double angle identity.

it comes from the sum identity for sine ...

$\sin(2t) = \sin(t+t) = \sin{t}\cos{t} + \cos{t}\sin{t} = 2\sin{t}\cos{t}$