Show that
(sin8 A -cos8 A)
= (2 sin2 A - 1) (1 - 2 sin2 A cos2 A).
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Answer:
Step-by-step explanation:
Sin⁸A - Cos⁸A = (Sin⁴A)² - (Cos⁴A)²
= (Sin⁴A - Cos⁴A)(Sin⁴A + Cos⁴A)
= [(Sin²A)² - (Cos²A)²][(Sin²A + Cos²A)² - 2Sin²ACos²A]
= [(Sin²A+Cos²A)(Sin²A -Cos²A)][ 1 - 2Sin²ACos²A]
= (Sin²A -Cos²A)(1 - 2Sin²ACos²A)
= (Sin²A - 1 + Sin²A)(1 - 2Sin²ACos²A)
= (2Sin²A - 1)(1 - 2Sin²ACos²A)
Hence proved.
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