SOLUTION: Determine the constants a and b so that {{{ (-3+4 cos^(2) x)/ (1-2 sin x) = a+b sin x }}} for all values of x.

Question 1192560: Determine the constants a and b so that for all values of x.
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
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Determine the constants a and b so that for all values of x.
~~~~~~~~~~~~~~~~~

Transform the numerator step by step

     =  =  =  = .


So, your fraction now is

     = .


Cancel the factors ((1-2*sin(x)) in both the numerator and denominator.  You will get then

     =  = 1 + 2*sin(x).


It is just the form which you need.  So,  a= 1,  b= 2.


ANSWER.  a= 1,  b= 2.

Solved.

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