SOLUTION: Simplify the expression. (cos˛x + sin˛x)/(cot˛x - cosec˛x)

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Question 1086800: Simplify the expression.

(cos˛x + sin˛x)/(cot˛x - cosec˛x)
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
(cos˛x + sin˛x)/(cot˛x - cosec˛x)

(cos˛x + sin˛x) ÷ (cot˛x - cosec˛x)

Use the identity 

              cos˛q + sin˛q = 1

1 ÷ (cot˛x - cosec˛x)

Use the identities
 
              cotq = cosq/sinq and
              cosecq = 1/sinq

1 ÷ (cos˛x/sin˛x - 1/sin˛x)

1 ÷ (cos˛x - 1)/sin˛x

Use the identity again

              cos˛q + sin˛q = 1, solved for cos˛q
              cos˛q = 1 - sin˛q 

1 ÷ (1 - sin˛x - 1)/sin˛x

1 ÷ -sin˛x/sin˛x

1 ÷ -1

-1

Edwin
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