cos ^2 A (3 - 4 cos ^2 A)^2 + sin ^2 A( 3 - 4 sin ^2 A) ^2 equal to

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Solution

Expanding the square and brackets =9 cos²A + 16 cos⁶A -24 cos⁴A + 9 sin²A + 16 sin⁶A -24 sin⁴A

= 9 + 16 (sin^6 A + cos^6 A) -24 ( sin⁴A + cos⁴A)

=

= 9 + 16 (sin²A + cos²A) (sin⁴A + cos⁴A - sin²A cos²A) -24(sin⁴A + cos⁴A)

=

= 9 -8(sin⁴A + cos⁴A + 2sin²A cos²A)

= 9 - 8(sin²A + cos²A)²
= 9 - 8*(1)²
= 9-8
= 1

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