Use a double-angle formula to find the exact value of when .

Question

Use a double-angle formula to find the exact value of  when  .

Quizplus · Accepted Answer

Using the double-angle formula, we have:
$$\cos(2x) = 2\cos^2(x) - 1$$
Letting $x = \frac{11eb80b1_afcd_83be_a291_3fa03f0077ef_TB8633_11}{2}$, we get:
\begin{align*}
\cos\left(11eb80b1_afcd_5cad_a291_7389288e5729_TB8633_11ight) &= \cos(2x) \
&= 2\cos^2(x) - 1 \
&= 2\cos^2\left(\frac{11eb80b1_afcd_83be_a291_3fa03f0077ef_TB8633_11}{2}ight) - 1 \
&= 2\left(\frac{3}{5}ight)^2 - 1 \
&= \frac{9}{25} - 1 \
&= -\frac{16}{25}
\end{align*}
Therefore, the correct answer is (D) 11eb80b1_afcd_d1e2_a291_6b2ad5bba13c_TB8633_11.

Use a Double-Angle Formula to Find the Exact Value of