Trigonometry
What is the value Cos2A(3-4Cos2A)2+Sin2A(3-4Sin2A)2
What is the value Cos2A(3-4Cos2A)2+Sin2A(3-4Sin2A)2
1 Answer
Arun
When expanding
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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