prove that (sinx+cosx)^2=1+sin2xidentities

Expert Answers
hala718 eNotes educator| Certified Educator

`(sinx+cosx)^2 = 1+sin2x`

First we will expand the square root.

`==> sin^2 + 2sinxcosx + cos^2 x = 1+ sin2x`

``We know that `sin^2 x + cos^2 x = 1`

`==gt 1 + 2sinxcosx = 1+ 2sinx`

`` Also, we know that: `2sinxcosx = sin2x`

```==gt 1 + sin2x = 1+ 2sinx` ..............q.e.d