Answer:
7/25
Explanation:
Let
so we have

As
, we'll have
![\cos[2\arcsin((3)/(5))]=\bigr[\cos(\arcsin((3)/(5)))\bigr]^2-\bigr[(\sin(\arcsin((3)/(5)))\bigr]^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/1lh6varpejziauzuxao5o5is6r5175qs2b.png)
To determine
, construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since
, then
. If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus,
. This means that
.
Hence,
![\cos[2\arcsin((3)/(5))]=((4)/(5))^2-((3)/(5))^2=(16)/(25)-(9)/(25)=(7)/(25)](https://img.qammunity.org/2023/formulas/mathematics/high-school/q2b2ll326kf7xr3l4rtgriemvya9cjtbh7.png)