Question

Prove (Cos²A)³ - (sin²A)³ = cos2A (1- 1/4 Sin²2A)

Answer 1

Answer:

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Answer 2

Answer:

(cos²A)³-(sin²A)³=cos2A[1-(1/4)sin²2A]

Step-by-step explanation:

LHS = (cos²A)³-(sin²A)³

= (cos²A-sin²A)[(cos²A)²+cos²Asin²A+(sin²A)²]

/* By algebraic identity:

a³-b³ =(a-b)(a²+ab+b²) */

= cos2A[(cos²A)²+2cos²Asin²A+(sin²A)²-sin²Acos²A]

/* cos²A-sin²A = cos2A */

= cos2A[(cos²A+sin²A)²-sin²Acos²A]

= cos2A[1-(4sin²Acos²A)/4]

= cos2A[1-(2sinAcosA)²/4]

=cos2A[1-(1/4)sin²2A]

= RHS

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