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Trigonometric identities - 11

tan^4(x) + tan^2(x) = sec^4(x) - sec^2(x)
The left hand side of the equation contains tan raised to the power of 4 and 2. tan^4(x) can be written as (tan^2(x))^2, so the left hand side can be written as:

(tan^2(x))^2 + tan^2(x)
From the identity 1 + tan^2(x) = sec^2(x), it follows that tan^2(x) = sec^2(x) - 1.
(sec^2(x) - 1)^2 + sec^2(x) - 1
Apply the algebraic identity (a - b)^2 = a^2 + b^2 - 2ab to (sec^2(x) - 1)^2
sec^4(x) + 1 - 2sec^2(x) + sec^2(x) - 1
Simplify by adding like terms.
sec^4(x) - sec^2(x)
... which is the right hand side of the equation

Trigonometric identities applied: