SOLUTION: He all, can you please help me verifying this identity step by step?: sin(3α)=3sin(α)-4sin^3(α) Thank you very much in advance RB

Algebra ->  Trigonometry-basics -> SOLUTION: He all, can you please help me verifying this identity step by step?: sin(3α)=3sin(α)-4sin^3(α) Thank you very much in advance RB       Log On


   

Question 1031286: He all,
can you please help me verifying this identity step by step?:
sin(3α)=3sin(α)-4sin^3(α)
Thank you very much in advance
RB
Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
.
He all,
can you please help me verifying this identity step by step?:
sin(3α)=3sin(α)-4sin^3(α)
Thank you very much in advance
RB
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Do you know this formula:  sin%28alpha+%2B+beta%29 = sin%28alpha%29%2Acos%28beta%29+%2B+cos%28alpha%29%2Asin%28beta%29 ?

Apply it one time, and you will get

sin%282alpha%29 = 2%2Asin%28alpha%29%2Acos%28alpha%29,

cos%282alpha%29 = cos%5E2%28alpha%29+-+sin%5E2%28alpha%29 = 1+-+sin%5E2%28alpha%29+-+sin%5E2%28alpha%29 = 1+-+2%2Asin%5E2%28alpha%29.

Apply it one more time, and you will get

sin%283alpha%29 = sin%28alpha%29%2Acos%282alpha%29+%2B+cos%28alpha%29%2Asin%282alpha%29 = 
                  
          =  = 

          = sin%28alpha%29+-+2%2Asin%5E3%28alpha%29+%2B+2%2Asin%28alpha%29%2Acos%5E2%28alpha%29 = 

          = sin%28alpha%29+-+2%2Asin%5E3%28alpha%29+%2B+2%2Asin%28alpha%29%2A%281-sin%5E2%28alpha%29%29 = 

          = 3%2Asin%28alpha%29+-+4%2Asin%5E3%28alpha%29.