SOLUTION: cos2xcosx+sin2xsinx=1 I have to solve this problem in terms of the unit circle by using the Double Angle Identities, but I have no idea how to solve the problem after I plug the

Algebra ->  Trigonometry-basics -> SOLUTION: cos2xcosx+sin2xsinx=1 I have to solve this problem in terms of the unit circle by using the Double Angle Identities, but I have no idea how to solve the problem after I plug the      Log On


   

Question 79822This question is from textbook Algebra 2 with Trigonometry
: cos2xcosx+sin2xsinx=1
I have to solve this problem in terms of the unit circle by using the Double Angle Identities, but I have no idea how to solve the problem after I plug them in. So far I have: (cos^2x-sin^2x)*(cosx)+(2sinx-cosx)*(sinx)=1 Is this even close to being on the right track? If someone could just help me get to what sinx and cosx equal I can find the radian angles from there. Thanks!!!
This question is from textbook Algebra 2 with Trigonometry

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

cos(2x)cos(x) + sin(2x)sin(x) = 1

You are going about it wrong.  You were
expected to recognize that the left side 
of that equation looks very much 
like the right side of the double
angle identity:

cos(A-B) = cos(A)cos(B) + sin(A)sin(B)

where A = 2x and B = x

So the left side of your original equation
can be replaced by cos(2x-x) from the left
side of the identity.

and immediately you can write

  cos(2x-x) = 1

     cos(x) = 1

So the answer is 

          x = 0 

Or, if your teacher wants all real solutions it is 

          x = 2np for all integers n.

Edwin