Question

Use a double-angle formula to find the exact value of cos 2u when sinu = 7/25

Please refer to photo

Answer 1

Option (c),
`{(527)/(625) }`

Explanation:

Use a double-angle formula to find the exact value of cos(2u) when sin(u) = 7/25.

`\boxed{\left\begin{array}{ccc}\text{\underline{The Double-Angle Identity for Cosine:}}\\\\\cos(2A)=\boxed{\cos^2(A)-\sin^2(A)} \ \text{or} \ \boxed{2\cos^2(A)-1} \ \text{or} \ \boxed{1-2\sin^2(A)}\end{array}\right }`

We have,

`\cos(2u)`

Applying the double-angle identity:

`\Longrightarrow 1-2\sin^2(u)`

Evaluating the sine with the given information:

`\Longrightarrow 1-2((7)/(25) )^2\\\\\\\Longrightarrow 1-2((49)/(625))\\\\\\\Longrightarrow 1-(98)/(625)\\\\\\\Longrightarrow \boxed{\boxed{(527)/(625) }}`

Thus, the problem is solved.