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

`(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=(3-4\cos(2x)+\cos(4x))/(8)`

Therefore:

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

An equivalent expression is:

`(3[3-4\cos(2x)+\cos(4x)])/(4)`