[SOLVED] Double angle problem

**brentwoodbc** · May 7th 2009, 02:43 PM

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.

**Prove It** · May 7th 2009, 02:49 PM

Originally Posted by brentwoodbc

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.

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

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

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

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.

**brentwoodbc** · May 7th 2009, 02:54 PM

Awesome thank you.

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