SOLUTION: verify trigonometric functions: (1-sin x)/(1+sin x) = (sec x

SOLUTION: verify trigonometric functions: (1-sin x)/(1+sin x) = (sec x - tan x)^2

Question 205343: verify trigonometric functions:
(1-sin x)/(1+sin x) = (sec x - tan x)^2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
verify trigonometric functions:
(1-sin x)/(1+sin x) = (sec x - tan x)^2
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On the left side, multiply numerator and denominator by 1-sinx to get:
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(1-sinx)^2/(1-sin^2(x)) = (secx-tanx)^2
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Modify the left side:
(1 - 2sinx + sin^2(x))/cos^2(x) = (secx-tanx)^2
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Modify the left side:
(sec^2(x)) - 2tanxsec(x) + tan^2(x)) = (secx-tanx)^2
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Factor the left side:
(sec(x)-tan(x))^2 = (secx-tanx)^2
=========================================
Cheers,
Stan H.
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