Answer:
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:
Answer: True
