[SOLVED] Double angle problem

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• May 7th 2009, 02:43 PM
brentwoodbc
[SOLVED] Double angle problem
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.
• May 7th 2009, 02:49 PM
Prove It
Quote:

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.
• May 7th 2009, 02:54 PM
brentwoodbc
Awesome thank you.