Question

Find the value of 2 (sin⁶A + cos⁶ A) – 3 (sin⁴A + cos⁴A)

Answer 1

Step-by-step explanation:

2(sin^6A+cos^6A)-3(sin^4A+cos^4A)

=2{(sin^2A)^3+(cos^2A)^3} -3{(sin^2A)^2+(cos^2A)^2}

=2{(sin^2A+cos^2A)^3-3sin^2Acos^2A(sin^2A+cos^2A)} -3{(sin^2A+cos^2A)^2-2sin^2Acos^2A}

=2(1-3sin^2Acos^2A)-3(1-2sin^2Acos^2A)

=2-6 sin^2Acos^2A-3+6sin^2Acos^2A

=2-3=-1