Help proving this expression is equal..

**Manizzle** · November 26th 2008, 01:24 PM

Prove that [sin x + cos x]^2 = 1 + sin 2x

**skeeter** · November 26th 2008, 02:36 PM

Originally Posted by Manizzle

Prove that [sin x + cos x] = 1 + sin 2x

I think you mean ...

$(\sin{x} + \cos{x})^2 = 1 + \sin(2x)$

**vincisonfire** · November 26th 2008, 04:13 PM

If that's not what he means then his book must be wrong.

**Manizzle** · November 26th 2008, 05:50 PM

yes i'm sorry thats what i meant, my superscript didn't work with the font i had on here sorry guys

**skeeter** · November 27th 2008, 03:33 AM

$(\sin{x} + \cos{x})^2 = 1 + \sin(2x)$

square the left side ...

$\sin^2{x} + 2\sin{x}\cos{x} + \cos^2{x}$

rearrange a bit ...

$(\sin^2{x} + \cos^2{x}) + 2\sin{x}\cos{x}$

now, you should know what the sum of the first two terms is ... also, look up the double angle formula for sine to deal with the last term.

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