If cos^4 A + cos^2 A =1, then prove that: tan^4 A+ tan^2 A =1.

Answer: 



So, to solve this question, first you need to see the image. We have
Cos⁴A + cos²A = 1
When we send cos²A to the right side

Cos⁴A = 1- cos² A

And we know,
Sin²A = 1 - cos²A

So,
Cos⁴A = sin²A
When we divide both by cos²A

We get
Cos²A = tan²A. [ TanA = sinA/cosA ]

When we multiply both sides by 1/ cos²A

We get 1 = tan²A * sec²A [ sec²A = 1/ cos²A]

And, sec²A = tan²A + 1
When we simplify this, we get

1 = tan⁴A + tan²A which is our right hand side.

Therefore, you can solve this Trigonometric Identity, If cos^4 A + cos^2 A =1, then prove that: tan^4 A+ tan^2 A =1
In Trigonometry of Mathematics.

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