SOLUTION: {{{ cos x + sin x = 1 + sin 2x }}} I'd like minimal help, just a hint so I can do it easily. Thanks!!

Algebra ->  Trigonometry-basics -> SOLUTION: {{{ cos x + sin x = 1 + sin 2x }}} I'd like minimal help, just a hint so I can do it easily. Thanks!!      Log On


   

Question 961085: +cos+x+%2B+sin+x+=+1+%2B+sin+2x+
I'd like minimal help, just a hint so I can do it easily. Thanks!!
Found 2 solutions by amarjeeth123, Edwin McCravy:
Answer by amarjeeth123(570) About Me  (Show Source):
You can put this solution on YOUR website!
cosx+sinx=1+sin2x
cosx+sinx=1+2sinxcosx
cosx+sinx=sinx^2+cosx^2+2sinxcosx (since sinx^2+cosx^2=1)
cosx+sinx=(sinx+cosx)^2
Solving we get,
sinx+cosx=1
x=0 degrees or x=90 degrees

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor did not get all the solutions.  You can't get
all the solutions from that last step "sinx+cosx=1"

+cos%28x%29+%2B+sin%28x%29%22%22=%22%221+%2B+sin%282x%29+

Do it this way:

1. Square both sides.
2. Use cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1
3. Cancel 1's on both side
4. Get 0 on one side.
5. use sin%5E2%28theta%29=1-cos%5E2%28theta%29
6. Factor and use zero-factor property.

If you have trouble, tell me in the thank-you note below.
I'll get back to you.  Free of charge of course. I do this
for fun, not for money! 

Edwin