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3 years ago

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

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

8 0

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

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Using the pythagorean theorem we know:

144=x^2+h^2, x^2=144-h^2, x=√(144-h^2) now we can use this in our inequality for x

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3 years ago

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The correct option is:

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We can see that the bottom width of the trapezoid is 9 inches, the top width of the trapezoid is 5 inches, and it has a height of 2 inches.

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3 years ago

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)