Cos^6A+sin^6A=1/4 (1+3cos^2 2A)=1/8 (5+3cos4A)

cos^6A+sin^6A=1/4 (1+3cos^2 2A)=1/8 (5+3cos4A) = True

Step-by-step explanation:

Solve for A:

cos^6(A) + sin^6(A) = 1/4 (3 cos^2(2 A) + 1)

Hint: | Expand out terms of the right hand side.

1/4 (3 cos^2(2 A) + 1) = 3/4 cos^2(2 A) + 1/4:

cos^6(A) + sin^6(A) = 3/4 cos^2(2 A) + 1/4

Hint: | Move everything to the left hand side.

Subtract 3/4 cos^2(2 A) + 1/4 from both sides:

-1/4 + cos^6(A) - 3/4 cos^2(2 A) + sin^6(A) = 0

Hint: | Write the left hand side as a single fraction.

Bring -1/4 + cos^6(A) - 3/4 cos^2(2 A) + sin^6(A) together using the common denominator 4:

1/4 (-1 + 4 cos^6(A) - 3 cos^2(2 A) + 4 sin^6(A)) = 0

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides by 4:

-1 + 4 cos^6(A) - 3 cos^2(2 A) + 4 sin^6(A) = 0

Hint: | Rewrite the left hand side.

Expand trigonometric functions:

0 = 0

Hint: | Look for a true statement.

0 = 0 is trivially true:

True

the answer is 2/54

step-by-step explanation: