Use the Power-Reducing Formulas
-$\sin ^ { 4 } x$
A) $\frac { 3 } { 8 } - \frac { 1 } { 2 } \cos 2 x + \frac { 1 } { 8 } \cos 4 x$
B) $\frac { 3 } { 2 } - \frac { 3 } { 2 } \cos 2 x$
C) $\frac { 3 } { 2 } - 2 \cos 2 x + \frac { 1 } { 2 } \cos 4 x$
D) $\frac { 3 } { 8 } + \frac { 5 } { 8 } \cos 2 x$

Question

Quizplus · Accepted Answer

To find the power-reducing formula for $\sin^4x$, we start with the double angle formula for cosine, $\cos 2x = 1 - 2\sin^2x$, and then apply the power-reducing formula to express $\sin^4x$ in terms of $\cos 2x$ and $\cos 4x$. The correct expression is $\frac{3}{8} - \frac{1}{2}\cos 2x + \frac{1}{8}\cos 4x$, which simplifies the fourth power of sine into a form involving the first and second powers of cosine.

Use the Power-Reducing Formulas - sin⁡4x\sin ^ { 4 } xsin4x

Use the Power-Reducing Formulas
- $\sin ^ { 4 } x$