Prove the following identity (sin^2x-tan^2x) / (cos^2- cot^x) = tan^6x?

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Prove the following identity (sin^2x-tan^2x) / (cos^2- cot^x) = tan^6x?

2007-10-23 07:29:02 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

1 answers

(sin² x - tan² x)/(cos² x - cot² x)
(sin² x cos² x - sin² x)/(cos⁴ x - cos² x cot² x)
sin² x (cos² x - 1)/(cos⁴ x - cos² x cot² x)
sin⁴ x/(cos⁴ x - cos² x cot² x)
sin⁶ x/(cos⁴ x sin² x - cos⁴ x)
sin⁶ x/(cos⁴ x (sin² x - 1))
sin⁶ x/cos⁶ x
tan⁶ x

Q.E.D.

2007-10-23 07:46:44 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋