(tan^2 x - 1) / sec^2 x = (tan x -cot x) / ( tan x + cot x)
Working with the right side Working with the left side
sin x /cosx - cos x / sin x tan^2 x - 1 / ( 1 /cos^2x)
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sin x / cos x + cos x /sin x cos^2 x ( sin^2 x / cos ^2 x - 1)
(sin^2 x - cos ^2x) / (sin x cos x)
___________________________ sin^2 x - cos ^2 x
(sin^2 x + cos^2 x) / (sin x cos x)
(sin ^2 x - cos ^2 x)
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1
sin^2 x - cos ^2 x