SOLUTION: Prove the identity: {{{sin(2x)/(2sin(x))=cos^2(x/2) - sin^2(x/2)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity: {{{sin(2x)/(2sin(x))=cos^2(x/2) - sin^2(x/2)}}}      Log On


   

Question 1129548: Prove the identity: sin%282x%29%2F%282sin%28x%29%29=cos%5E2%28x%2F2%29+-+sin%5E2%28x%2F2%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sin%282x%29%2F%282sin%28x%29%29=cos%5E2%28x%2F2%29+-+sin%5E2%28x%2F2%29

Use the identity: cos%5E2%28theta%29-sin%5E2%28theta%29=cos%282theta%29
on the right side with theta=x%2F2 to rewrite the right
side as cos(x).

sin%282x%29%2F%282sin%28x%29%29=cos%28x%29

Now work with the left side.  [It's OK to do this, because you are
only working with one side AT A TIME, never BOTH sides together!!!]

Use the identity: sin%282theta%29=2sin%28theta%29cos%28theta%29 on the
left side:

2sin%28x%29cos%28x%29%2F%282sin%28x%29%29=cos%28x%29

Cancel:



cos%28x%29=cos%28x%29

Edwin