# Please help me to solve this, use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. #sin^4(5x) cos^2(5x)#?

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To rewrite the expression in terms of first powers of the cosines of multiple angles, we can use the power-reducing formula for sine and cosine:

sin^2(x) = (1 - cos(2x))/2 cos^2(x) = (1 + cos(2x))/2

Substitute these formulas into the expression:

sin^4(5x) cos^2(5x) = (sin^2(5x))^2 cos^2(5x) = ((1 - cos(10x))/2)^2 ((1 + cos(10x))/2) = ((1 - cos(10x))^2 / 4) * ((1 + cos(10x)) / 2) = ((1 - 2cos(10x) + cos^2(10x)) / 4) * ((1 + cos(10x)) / 2) = (1 - 2cos(10x) + cos^2(10x)) * (1 + cos(10x)) / 8 = (1 + cos(10x) - 2cos(10x) - 2cos^2(10x)) / 8 = (1 - cos(10x) - 2cos^2(10x)) / 8

So, sin^4(5x) cos^2(5x) rewritten in terms of first powers of the cosines of multiple angles is:

(1 - cos(10x) - 2cos^2(10x)) / 8

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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