sec^4 α - 1 = 2 tan^2 α + tan^4 α | Prove | Sci-Pi

Prove that: sec^4 α - 1 = 2 tan^2 α + tan^4 α

Answer:

To prove: sec^4 α - 1 = 2 tan^2 α + tan^4 α

We need to analyze the LHS of the given question.

We have a^2 - b^2 which can be expanded as (a+b) ( a-b) which we did in the process.

Using identity: sec^2 x - tan^2 x = 1

And sec^2 x = 1 + tan^2 x

We solved the above question and proved that the LHS is equal to the RHS.

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