Use the power reduction formulas to rewrite the expression. (Hint: Your answer should not contain any exponents greater than 1.)

Mathematics

1 answer:

WINSTONCH [101]1 year ago

8 0

The formulas in question are

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

Then

sin⁴(4x) = (sin²(x))²

… = ((1 - cos(2x))/2)²

… = (1 - 2 cos(2x) + cos²(2x))/4

… = (1 - 2 cos(2x) + (1 + cos(4x))/2)/4

… = 1/4 - 1/2 cos(2x) + (1 + cos(4x))/8

… = 3/8 - 1/2 cos(2x) + 1/8 cos(4x)

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Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.

Sin α = opposite side / hypotenuse

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