Question 41592
<pre><font size = 5><b>Simplify these expressions:

   2cotB
———————————
 1 + cot²B

Use the identity cot<font face = "symbol">q</font> = cos<font face = "symbol">q</font>/sin<font face = "symbol">q</font> to replace
the numerator

Use the identity 1 + cot²<font face = "symbol">q</font> = csc²<font face = "symbol">q</font> to replace 
the denominator

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

Use identity csc<font face = "symbol">q</font> = 1/sin<font face = "symbol">q</font> 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     <s>sin²B</s>
——————— × ———————
 <s>sinB</s>        1
  1 

    2cosBsinB

Edwin
AnlytcPhil@aol.com</pre>