SOLUTION: Please help me prove this equation ((1-cos4x)/(1+cos4x)) + 1 = sec^2(2x)

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]

RELATED QUESTIONS
cos4x-sen4x/1-tan4x=cos4x (answered by Alan3354)

please help me prove identity for... (answered by jsmallt9)

Can you please help me to solve this problem. The question reads; Find all solutions of... (answered by Fombitz)

Prove that: Sin^4x =1�8... (answered by advanced_Learner,Alan3354)

Prove the identity of... (answered by ikleyn)

Prove: Cos4x = 8Cos^4(x) - 8Cos^2(x) + 1 Thank you in advance (answered by MathLover1)

Sin^4x = 1�8... (answered by robertb,advanced_Learner)

please help me prove this equation:... (answered by vicgonzerx)

Hello, I'm a little stuck... The question is: prove that... (answered by jsmallt9)