SOLUTION: Prove the identity: {{{tan(x) /( 1 + (tan(x))^2) = sin(x)cos(x)}}} (x is theta)

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity: {{{tan(x) /( 1 + (tan(x))^2) = sin(x)cos(x)}}} (x is theta)      Log On


   

Question 138815: Prove the identity: tan%28x%29+%2F%28+1+%2B+%28tan%28x%29%29%5E2%29+=+sin%28x%29cos%28x%29 (x is theta)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm only manipulating the left side. I'm not touching the right side. I'm only showing it for comparison.




Start with the given equation




Replace with


Simplify


Multiply both the numerator and denominator by the LCD . This will clear out the denominators in both the numerator and the denominator.



Distribute and multiply




Replace with 1



Simplify


So we've just proven that



is an identity.