SOLUTION: What is the value of cos(2α) , if sin(3α) =2 sin(α)?

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Question 1126750: What is the value of cos(2α) , if sin(3α) =2 sin(α)?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

What is the value of , if

?

use the following identity:

factor it:

use identity




then we have


...simplify, divide by





Answer by ikleyn(52793)   (Show Source): You can put this solution on YOUR website!
.

                The solution by the tutor @MathLover1 is not exactly correct,

                so I came to fix it. 


Start from this basic identity


    sin(3a) = 3*sin(a) - 4*sin^3(a).


We are given that


    3*sin(a) - 4*sin^3(a) = 2*sin(a).


It implies


     = 0.


So, either  sin(a) = 0   or    = 0;  the last is equivalent to   = .


Case 1.  If  sin(a) = 0,  then  cos(2a) =  = 1.


Case 2.  If   = ,  then  cos(2a) =  =  = .


Answer.  If  sin(3a) =2*sin(a),  then EITHER  cos(2a) = 1  OR  cos(2a) = .

Solved.


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