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

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Question 525073: verify: (1-sin x)/(1+sin x)=(sec x-tan x)^2
Answer by lwsshak3(11628) About Me  (Show Source):
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verify: (1-sin x)/(1+sin x)=(sec x-tan x)^2
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Starting with left side:
(1-sin x)/(1+sin x)
multiply top and bottom by (1-sin). This makes the bottom a difference of squares.
[(1-sin)/(1+sin)][(1-sin)/(1-sin)
(1-sin)^2/(1-sin^2)
(1-2sin+sin^2)/cos^2
1/cos^2-2sin/cos^2+sin^2/cos^2
sec^2-2sin/cos^2+tan^2
sec^2-2/cos*sin/cos+tan^2
sec^2-2sec*tan+tan^2
(sec-tan)^2
Verified: left side=right side