it says to prove
1+sin2x=(sinx+cosx)^2
so I'm stuck
i have tried
1+2sinxcosx=1-2sin^2x
and
1+2sinxcosx=cos2x
...
I need help. Thanks.
$\displaystyle (\sin{x}+\cos{x})^2 = \sin^2{x} + 2\sin{x}\cos{x} + \cos^2{x}$
$\displaystyle = \sin^2{x} + \cos^2{x} + 2\sin{x}\cos{x}$
$\displaystyle = 1 + \sin{(2x)}$ because $\displaystyle \sin^2{x} + \cos^2{x} = 1$ and $\displaystyle 2\sin{x}\cos{x} = \sin{(2x)}$.
With these sorts of problems it is best to work on the easier looking side and make it look like the other one. Knowing which one looks easiest takes practice though.