Question 1075296: Please help me prove this equation
((1-cos4x)/(1+cos4x)) + 1 = sec^2(2x)
Answer by Aaragorn(2)   (Show Source):
You can put this solution on YOUR website! We know that,
cos 2x = cos^2(x) - sin^2(x) = 2cos^2(x) - 1 = 1 - 2sin^2(x)
Therefore,
cos 2x = 2cos^2(x) - 1
=> 1 + cos 2x = 2cos^2(x)
Also,
cos 2x = 1 - 2sin^2(x)
=> 1 - cos 2x = 2sin^2(x)
Therefore,
1 - cos 4x = 1 - cos 2(2x) = 2sin^2(2x)
1 + cos 4x = 1 + cos 2(2x) = 2sin^2(2x)
Left had side of equation is..
(1 - cos 4x)/(1 + cos 4x) + 1
=> [ 2sin^2(2x) ] / [ 2sin^2(2x) ] + 1
=> tan^2(2x) + 1
By formula, tan^2(x) + 1 = sec^2(x)
Therefore,
tan^2(2x) + 1 = sec^2(2x) = Right hand side
[HENCE PROVED]
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