SOLUTION: Please help, I am so confused. The question reads: complete the identity {{{tan(theta/2)}}} and my answer options are a) {{{tan(theta)/(csc(theta)-1))}}} b) {{{tan(theta)/(csc

Algebra ->  Trigonometry-basics -> SOLUTION: Please help, I am so confused. The question reads: complete the identity {{{tan(theta/2)}}} and my answer options are a) {{{tan(theta)/(csc(theta)-1))}}} b) {{{tan(theta)/(csc      Log On


   



Question 320980: Please help, I am so confused.
The question reads: complete the identity tan%28theta%2F2%29
and my answer options are
a) tan%28theta%29%2F%28csc%28theta%29-1%29%29
b) tan%28theta%29%2F%28csc%28theta%29%2B1%29%29
c) tan%28theta%29%2F%28sec%28theta%29%2B1%29%29
d) tan%28theta%29%2F%28sec%28theta%29-1%29%29

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

Look in your textbook or notes, or go to

http://mathworld.wolfram.com/Half-AngleFormulas.html

and you'll find that

tan%28theta%2F2%29%22=%22sin%28theta%29%2F%281%2Bcos%28theta%29%29

We observe that all the choices have tan%28theta%29 on the top,
and since we know that tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
we can make the top of the right side of the above identity into
tan%28theta%29 by dividing every term in the top and bottom by cos%28theta%29.


tan%28theta%2F2%29%22=%22sin%28theta%29%2F%281%2Bcos%28theta%29%29%22=%22

and since 1%2Fcos%28theta%29=sec%28theta%29, we have

tan%28theta%2F2%29%22=%22sin%28theta%29%2F%281%2Bcos%28theta%29%29%22=%22%22=%22tan%28theta%29%2F%28sec%28theta%29%2B1%29%29%22=%22%22answer_option_%28c%29%22

Edwin