SOLUTION: If cos α / cos β = a, sin α / sin β = b, then sinČβ is equal to

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Question 1040397: If cos α / cos β = a, sin α / sin β = b, then sinČβ is equal to
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
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If cos(alpha)/cos(beta) = a, sin(alpha)/sin(beta) = b, then sinČ(beta) is equal to
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
From    =   you have   =   and then   = .     (1)

Having this, I would say the problem is just solved, because I just expressed  . 

But I understand that you want me to express    via  "a"  and "b"  and exclude  ,  although 
it is not stated directly and implicitly in the problem formulation (which is the author's fault).

So I will continue.


From the condition, we have this line of identities 

 =   --->   =                                         (2)

and this line 

 =  =   --->   =   --->  

 =   --->   = .                  (3)

Next substitute the last identity of (3) into the last identity of (2). You will get

 =   --->   =   --->   = .     (4)

Now we can complete (1) by substituting the found value of  from (4) into (1). You will get

 = .

Answer.   = .


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