SOLUTION: sin(x)/2cos(X)/2(1-2sin^2(x)/2) The answer in my book is 1/4 sin(2x) I tried solving it but I can't seem to figure out the answer.

Algebra ->  Trigonometry-basics -> SOLUTION: sin(x)/2cos(X)/2(1-2sin^2(x)/2) The answer in my book is 1/4 sin(2x) I tried solving it but I can't seem to figure out the answer.      Log On


   

Question 1144154: sin(x)/2cos(X)/2(1-2sin^2(x)/2)
The answer in my book is 1/4 sin(2x)
I tried solving it but I can't seem to figure out the answer.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sin(x)/2cos(X)/2(1-2sin^2(x)/2)
The answer in my book is 1/4 sin(2x)
I tried solving it but I can't seem to figure out the answer.
------------
1) it's ambiguous. add parentheses.
2) there's nothing to solve. Problems are solved. Equations are solved. This is neither.
3) You didn't ask a question or make a request.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

First,   sin(x/2)cos(x/2) = %281%2F2%29%2Asin%28x%29.


Second,  1-2sin^2(x/2)  = cos(x).


Therefore,  sin(x/2)cos(x/2)(1-2sin^2(x/2)) = %281%2F2%29%2Asin%28x%29%2Acos%28x%29 = %281%2F4%29%2Asin%282x%29.    ANSWER

------------

You need to know basic Trigonometry formulas for multiple arguments  (for double arguments,  in this case).

See the lesson
    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS
in this site.