SOLUTION: sin(3x)/sin x= 2 cos(2x)+1 cot x/(csc x+1)= (csc x -1)/cot x

Question 635009: sin(3x)/sin x= 2 cos(2x)+1

cot x/(csc x+1)= (csc x -1)/cot x

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

 = 

We work with the left side

We write 3x as 2x+x

 

Use the identity 
with  and 



Break into the sum of two fractions with the same denominator
 
 + 

Cancel the sin(x)'s in the second term

 + 

 + 

Use the identity  for 

 + 

Cancel the sin(x)'s in the first term

 + 

 + 

 + 

Use the identity  solved for 
or 

 + 

Combine like terms:



--------------------------

 = 

We work with the left side:

Multiply the left sides by the conjugate of the denominator
over itself.  That is multiply by 

�





We use the identity  to replace the
 in the denominator.









Edwin

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