SOLUTION: Verify the identity. Justify each step. cot [theta - x/2] = - tan theta

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity. Justify each step. cot [theta - x/2] = - tan theta      Log On


   

Question 627975: Verify the identity. Justify each step.
cot [theta - x/2] = - tan theta
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I must assume that the "x/2" is supposed to be pi%2F2. If what you posted is correct then I see no way to solve this.

cot%28theta-pi%2F2%29+=+-tan%28theta%29
Probably the quickest way to solve this is based on recognizing that theta+-+pi%2F2+=+-%28pi%2F2+-+theta%29. Substituting this in we have:
cot%28-%28pi%2F2-theta%29%29+=+-tan%28theta%29
Next we use the odd/even property for cot, cot(-x) = - cot(x), which allows us to "move" the negative out of the argument:
-cot%28pi%2F2-theta%29+=+-tan%28theta%29
Next we use another identity: cot%28pi%2F2-x%29+=+tan%28x%29%0D%0A%7B%7B%7B-tan%28theta%29+=+-tan%28theta%29
And we're finished!