Prove that (sinx + cosx)^2 = 1 + 2sinxcosx
Starting on the left hand side we can expand out the brackets to get:
(sinx + cosx)(sinx + cosx)
sin2x+sinxcosx+sinxcosx+cos2x
Grouping together the like terms we can rearrange it to be:
sin2x + cos2x + 2sinxcosx
We now have one of the terms on the right hand side. We only need to get the 1. If we remember our identity sin2x + cos2x = 1 we can remove the first two terms and replace them with a 1, giving us:
1 + 2sinxcosx, the same as the right hand side, therefore proving the two are equal
AG
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