Prove that: sec^4 Θ + tan^4 Θ = 1 + 2tan^2 Θ sec^2 Θ 

Answer:


This is a very simple Trigonometric question that you will ever get in Trigonometry. Here we have to use the algebraic formulas and Trigonometric identities.

Algebraic formulas used:
a^2 + b^2 = (a + b)^2 - 2 ab OR (a - b)^2 + 2 ab

We need to analyze which formula should be used here.
Let's see the RHS, we have (+ 2tan^2 Θ sec^2 Θ)

This means we need to use the formula of:

a^2 + b^2 = (a - b)^2 + 2 ab

And then we used the Trigonometric identity
I.e. sec^2 x - tan^2 x = 1

This way we can easily prove the given trigonometric identity.

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