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Home Q & A Board Science-Related Homework Help Mathematics
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riverviewguit riverviewguit
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11 years ago
The equation is y = (1 + cos^2x) / (1 - cos^2x)

The answer is supposed to be (4cosx) / (sin^3x)

Can somebody SHOW me how it is done, step by step? I know this involves the quotient rule, but I just can't figure it out. Any help is much appreciated.
Thanks for the help, I didn't properly recognize the part where 1 = sin^2 + cos^2.

And yes you guys are right, I forgot to add a - in front of the answer
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#1
11 years ago
y = (1 + cos^2(x)) / (1 - cos^2(x)

recall that 1 - cos^2(x) = sin^2(x)

Thus y = (1 + cos^2(x)) / sin^2(x)

split the fraction

y = ( 1 / sin^2(x))  + ( cos^2(x) / sin^2(x))

y = csc^2(x) + cot^2(x)

now differtentiate

y '  = 2 csc x ( - csc x cot x ) + 2cot x (- csc^2(x)

= -4 cot x  csc^2(x)

= - 4 (cos x / sin x)(1 / sin^2(x)

= - 4cos x / sin^3(x)
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RiyanRiyan
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11 years ago
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