Question

Hi this is part of my homework I'm struggling with so, if possible, please show me how to Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than one.6 sin⁴ x

Answer 1

Answer:

$\frac{3[3-4\cos(2x)+\cos(4x)]}{4}$

Explanation:

Given the trigonometric expression:

$6\sin ^4x$

By the power-reducing formula for the fourth power:

$\sin ^4x=\frac{3-4\cos(2x)+\cos(4x)}{8}$

Therefore:

$\begin{gathered} 6\sin ^4x=6\mleft[\frac{3-4\cos(2x)+\cos(4x)}{8}\mright] \\ =\frac{3}{4}\mleft[3-4\cos (2x)+\cos (4x)\mright] \\ \implies6\sin ^4x=\frac{3\lbrack3-4\cos (2x)+\cos (4x)\rbrack}{4} \end{gathered}$

An equivalent expression is:

$\frac{3[3-4\cos(2x)+\cos(4x)]}{4}$