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

Algebra ->  Trigonometry-basics -> SOLUTION: Determine the constants a and b so that (-3 + 4cos^2 x) / (1 - 2sinx) = (a + bsinx) for all values of x      Log On


   

Question 1177811: Determine the constants a and b so that (-3 + 4cos^2 x) / (1 - 2sinx) = (a + bsinx) for all values of x
Found 2 solutions by mananth, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(-3 + 4cos^2 x) / (1 - 2sinx) = (a + bsinx)


(-3+4(1-sin^2x))/ (1-2sinx)
((1-4sin^2x)/(1-2sinx)
(1+2sinx)(1-2sinx))/(1-2sinx)
1+2sinx = a+bsinx
comparing
a=1, b=2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28-3+%2B+4cos%5E2%28+x%29%29+%2F+%281+-+2sin%28x%29%29+=+%28a+%2B+b%2Asin%28x%29%29

%28-3+%2B+4cos%5E2%28+x%29%29+=+%28a+%2B+b%2Asin%28x%29%29+%281+-+2sin%28x%29%29+

-3+%2B+4cos%5E2%28+x%29+=+a+-+2a%2Asin%28x%29%2B+b%2Asin%28x%29-2b%2Asin%5E2%28x%29.......use cos%5E2%28+x%29=1-+sin%5E2%28+x%29

-3%2B4%281-+sin%5E2%28+x%29%29+=+a+-+2a%2Asin%28x%29%2B+b%2Asin%28x%29-2b%2Asin%5E2%28x%29

-3%2B4-+4sin%5E2%28+x%29+=+a+-+2a%2Asin%28x%29%2B+b%2Asin%28x%29-2b%2Asin%5E2%28x%29

1-+4sin%5E2%28+x%29+=+a+-+2a%2Asin%28x%29%2B+b%2Asin%28x%29-2b%2Asin%5E2%28x%29

1+-+%282sin%28x%29%29%5E2+=+-%282sin%28x%29+-+1%29+%28a+%2B+b%2A+sin%28x%29%29

-+%28%282sin%28x%29%29%5E2-1%29+=+-%282sin%28x%29+-+1%29+%28a+%2B+b%2A+sin%28x%29%29



2sin%28x%29%2B1=+++b%2Asin%28x%29+%2Ba+=> will be true for all values of x only if a=1 and b=2