dble angle ident: prove 1+sin2x=(sinx+cosx)^2 algebraically

[flyingfreedom]

Hi everyone
Prove algebraically:
1+sin2x=(sinx+cosx)^2

Work Done

I tried expanding the left side with the double angle identity for sine2x
so: 1+2sinxcosx=(sinx+cosx)^2
it looked closer but still not proved.
I have been trying to get the right side out of brackets but don't know
how. I don't think you can go sin²x+cos²x, because it doesn't
equal the same thing.
so I'm lost.help!

 

[tkhunny]

Re: double angle identity

Expand the right-hand side.

Use the Pythagorean identity to simplify.

Use the double angle identity you tried already to finish.