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how do you factor and simplify, tan^2 x - cot^2 x? please help!?
2 Answers
- Marley KLv 79 years agoFavorite Answer
you have the difference of two squares, so factor as such:
(tanx - cotx)(tanx + cotx)
however, simplify usually means to do the following:
write with sine and cosine:
(sin^2 x / cos^2 x) - (cos^2 x / sin^2 x)
get a common denominator and combine numerators:
(sin^4 x - cos^4 x) / (sinx cosx)^2
factor the numerator as difference of squares:
(sin^2 x + cos^2 x)(sin^2 x - cos^x) / (sinx cosx)^2
replace sin^2x + cos^2x with 1, and factor the difference of squares:
(sinx + cosx)(sinx - cosx) / (sinx cosx)^2
not so "simple", but that's it! ;)
- 9 years ago
If I remember right, you can use the "Perfect Square" principal. since both sides are squared you can change it to (tanx-cotx)(tanx+cotx)
