SOLUTION: simplify these expressions: (2cotB)/(1+cot^B) the answer is supposed to be 2cosBsinB but i have no idea how that occurs.

Algebra ->  Trigonometry-basics -> SOLUTION: simplify these expressions: (2cotB)/(1+cot^B) the answer is supposed to be 2cosBsinB but i have no idea how that occurs.       Log On


   

Question 41592: simplify these expressions:
(2cotB)/(1+cot^B)

the answer is supposed to be 2cosBsinB but i have no idea how that occurs.
Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify these expressions:

   2cotB
———————————
 1 + cot²B

Use the identity cotq = cosq/sinq to replace
the numerator

Use the identity 1 + cot²q = csc²q to replace 
the denominator

   2(cosB/sinB)
 ————————————————
      csc²B

Use identity cscq = 1/sinq to replace denominator
 

   2(cosB/sinB)
 ————————————————
     (1/sinB)²
 
   2cosB/sinB 
 ————————————————
     1/sin²B

 2cosB       1
——————— ÷ ———————
 sinB      sin²B

Invert and multiply

 2cosB     sin²B
——————— × ———————
 sinB        1

Cancel the sinB into the sin²B

           sinB  
 2cosB     sin²B
——————— × ———————
 sinB        1
  1 

    2cosBsinB

Edwin
AnlytcPhil@aol.com