Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain...

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Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 128 sin^2 x cos^2 x

SnapAndSolve AI · Accepted Answer

To rewrite the expression using power-reducing formulas, we use the identities:

sin² x = (1 - cos(2x))/2
cos² x = (1 + cos(2x))/2

Substitute these into the expression:

128 sin² x cos² x = 128 ((1 - cos(2x))/2) ((1 + cos(2x))/2)

Simplify the expression:

= 128 (1 - cos²(2x))/4

= 32 (1 - cos²(2x))

Using the identity 1 - cos²(2x) = sin²(2x), we get:

= 32 sin²(2x)

Finally, use the power-reducing formula again for sin²(2x):

= 32 (1 - cos(4x))/2

= 16 (1 - cos(4x))

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Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain...

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