Question

Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 40sin^2xcos^2x

Answer 1

Answer:

$x = 0.175\cdot (1-\cos 4\cdot \theta)$

Step-by-step explanation:

Let use the following trigonometric identities:

$\sin^{2}\theta = \frac{1-\cos 2\cdot \theta}{2} \\\cos^{2}\theta = \frac{1+\cos 2\cdot \theta}{2}$

Then, the equation is simplified by substituting its components:

$x = 1.40\cdot \left(\frac{1-\cos 2\cdot \theta}{2} \right)\cdot \left(\frac{1+\cos 2\cdot \theta}{2} \right)$

$x = 0.35\cdot (1-\cos^{2}2\cdot \theta)$

$x = 0.35\cdot \sin^{2}2\cdot \theta$

$x = 0.35\cdot \left(\frac{1-\cos 4\cdot \theta}{2} \right)$

$x = 0.175\cdot (1-\cos 4\cdot \theta)$

Answer 2

Answer:

(1/8) - (1/8)* [cos (4x)]

Step-by-step explanation:

We will apply the corresponding formulas and through algebra we will reach the result in the following steps:

Sin^2 (x) * Cos^2 (x) = {[1 - cos (2x)]/2}*{[1 + cos (2x)]/2}

Sin^2 (x) * Cos^2 (x) =[ 1 - cos^2 (2x)]/4

Sin^2 (x) * Cos^2 (x) = (1/4) - (1/4) * cos^2 (2x)

Sin^2 (x) * Cos^2 (x) =  (1/4) - (1/4) * {[1 + cos (2*2x)]/2}

Sin^2 (x) * Cos^2 (x) =  (1/4) - (1/8) * [1 + cos (4x)]

Sin^2 (x) * Cos^2 (x) =  (1/4) - (1/8) - (1/8)* [cos (4x)]

Sin^2 (x) * Cos^2 (x) =  (1/8) - (1/8)* [cos (4x)]