HI, I am having some trouble with proving identities. Could I have some help please.
sin^2x + cos^4x = cos^2x + sin^4x ← Manipulate L.S.
sin^2x + cos^4x = cos^2x + sin^4x ← Manipulate L.S.
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sin^2x + cos^4x = cos^2x + sin^4x
use Pythagorean Identity: sin²Θ+cos²Θ = 1
(1-cos²x) + (1-sin²x)(1-sin²x)
= 1-cos²x + 1 - 2sin²x + sin^4x
= 2-cos²x - 2 sin²x + sin^4x
= 2(1-sin²x) - cos²x + sin^4x
= 2cos²x - cos²x + sin^4x
= cos²x + sin^4x
QED
use Pythagorean Identity: sin²Θ+cos²Θ = 1
(1-cos²x) + (1-sin²x)(1-sin²x)
= 1-cos²x + 1 - 2sin²x + sin^4x
= 2-cos²x - 2 sin²x + sin^4x
= 2(1-sin²x) - cos²x + sin^4x
= 2cos²x - cos²x + sin^4x
= cos²x + sin^4x
QED