SOLUTION: Simplify completely {{{ ((Cos(x)+sin(x))^2-(cos(x)-sin(x))^2)/ (2sin(2x)) }}}

Question 451411: Simplify completely

Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
The top is a difference of two squares. Remember that In your case, a is cos(x)+sin(x), and b is cos(x)-sin(x). Substitute those in and the first parentheses is , which simplifies to 2cos(x). For the other, don't forget to distribute the subtraction: , which simplifies to 2sin(x). Thus, at this point we have: .
The double angle formula for sine says . The denominator is then . If we simplify the numerator and denominator, we have , which is, of course, 1 :)
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