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.
16 sin4x
16sin4x = _____

Answer 1

Answer:

$6-8cos2x+2cos4x$

Step-by-step explanation:

We are given that

$16sin^4 x$

We can write the given expression as

$16(sin^2x \times sin^2 x)$

$16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})$

By using the formula

$sin^2\theta=\frac{1-cos2\theta}{2}$

$4(1-cos2x)^2$

$4(1-2cos2x+cos^2(2x)$

Using the identity

$(a-b)^2=a^2+b^2-2ab$

$4(1-2cos2x+\frac{1+cos4x}{2})$

$4-8cos2x+2+2cos4x$

$6-8cos2x+2cos4x$

This is required expression.