This is for my trig class. Thanks for the help!
cos^2(x) / (1 - sin(x)) =
(1 - sin^2(x)) / (1 - sin(x)) =
(1 + sin(x)) * (1 - sin(x)) / (1 - sin(x)) =
1 + sin(x), x ≠ pi/2 + 2pi(n), n integer.
Rationalize the denominator and simplify: cos^2x / 1 - sinx
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3 Answers
COS ^2 x / (1 -SIN X ) =
Cos ^2 X . ( 1 + SIN X) /. (1 + Sin X) (1 - SIN X) =
/= 1- Sin^2 X
/ = Cos ^2X
! + Sin X.
Rationalization is not a proper word to use here. Because ( 1- Sin X) is not an irrational quantity.
cos^2(x)/[1-sin(x)]
multiply numerator and denominator by 1+sin(x)
[cos^2(x)][1+sin(x)]/[1-sin(x)][1+sin(x)]
cos^2(x)+cos^2(x)sin(x)/[1-sin^2(x)]
cos^2(x)+cos^2(x)sin(x)/cos^2(x) because 1=sin^2(x)+cos^2(x)
1+sin(x) is the answer
or
cos^2(x)/[1-sin(x)]=[1-sin^2(x)]/[1-sin(x)]
=[1-sin(x)][1+sin(x)]/[1-sin(x)]
=1+sin(x)
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