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

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Use a double-angle formula to find the exact value of cos 2u when sinu = 7/25 Please-example-1

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Answer:

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.

User Iamio
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