Question

$\huge\mathfrak\red{Question:-}$

Prove that :

Sin⁴Θ-Cos⁴Θ=1-2Cos²Θ

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Answer 1

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Sin⁴θ-Cos⁴θ=1-2Cos²θ

LHS=Sin⁴θ-Cos⁴θ

=(Sin²θ)²-(Cos²θ)²………………a²+b²=(a-b)(a+b)

=(Sin²θ-Cos²θ)(Sin²θ+Cos²θ)…………Sin²θ+Cos²θ=1

=(Sin²θ-Cos²θ)×1

=Sin²θ+Cos²θ-Cos²θ-Cos²θ

=Sin²θ+Cos²θ-2Cos²θ…………Sin²θ+Cos²θ=1

=1-2Cos²θ

=RHS

$<marquee>$♥Hence Proved♥

Answer 2

This is your answer.

Hope it will help you..