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value of Cos^2A {(3-4cos^2A)^2}+ Sin^2(A) {3-4Sin^2(A)}^2

value of Cos^2A {(3-4cos^2A)^2}+ Sin^2(A) {3-4Sin^2(A)}^2
 

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
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
 
Regards
Arun (askIITians forum expert)

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