Question

prove the following identity sin^ 6 A+ cos 6 A is equals to 1 - 3 sin square A cos square A​

Answer 1

Step-by-step explanation:

R.T.P: sin⁶A+cos⁶A=1+3sin²Acos²A

Proof: L.H.S: sin⁶A+cos⁶A= (sin²A)³+(cos²A)³

=(sin²A+cos²A)(sin⁴A+cos⁴A-sin²Acos²A)

since, a³+b³= (a+b)(a²+b²-ab)

          sin²A+cos²A=1

=((sin²A)²+(cos²A)²-sin²Acos²A)

=((sin²A+cos²A)²-2sin²Acos²A-sin²Acos²A)

since, a²+b²= (a+b)²- 2ab

=1-3sin²Acos²A

Hence, proved