Question

prove that

(cos^8∅ - sin^8∅) = (cos²∅ - sin²∅)(1 - 2 sin²∅ cos²∅)

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Answer 1

$\huge\underline{\underline{\mathfrak\red{Answer}}}$

To Prove

(cos^8∅ - sin^8∅) = (cos²∅ - sin²∅)(1 - 2 sin²∅ cos²∅)

Proving

L.H.S → (cos^8∅ - sin^8∅) = (cos⁴∅)² - (sin⁴∅)²

→ (cos⁴∅ + sin⁴∅)(cos⁴∅ - sin⁴∅)

→ [(cos²∅ + sin²∅)² - 2cos²∅sin²∅][cos²∅ + sin²∅](cos²∅ - sin²∅)

Since cos²∅ + sin²∅ = 1,

→ (1 - 2cos²∅ sin²∅)(cos²∅ - sin²∅) = R.H.S

Hence Proved