Pythagorean Identities

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Prove that:

1. (Sin^4 A - Cos^4 A) / (Sin^2 A - Cos^2 A) =1

2. (Cos x / 1-sin x) - (cos x / 1+sin x) = 2 tan x

Feb 8th, 2015

1. (Sin^4 A - Cos^4 A) = (Sin^2 A + Cos^2 A)(Sin^2 A - Cos^2 A) = (1)(Sin^2 A - Cos^2 A)

(Sin^2 A - Cos^2 A) / (Sin^2 A - Cos^2 A) = 1

2. (Cos x / 1-sin x) - (cos x / 1+sin x) = 2 tan x

Common denominator is (1-sin x)(1+sin x) = 1 - sin^2 x = cos^2 x

[Cos x (1 + sin x) - cos x ( 1-sin x)] / cos^2 x

= (cos x + cos x sin x - cos x + cos x sin x) / cos^2 x

= 2 cos x sin x / cos^2 x

= 2 sin x / cos x =  2 tan x


Feb 8th, 2015

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