**Objective:**Use the given conditions to find the exact values of \(\sin(2u)\), \(\cos(2u)\), and \(\tan(2u)\) using the double-angle formulas.**Given:**\[\cos(u) = -\frac{15}{17}, \quad \frac{\pi}{2} < u < \pi\]**Expressions to Find:**1. \(\sin(2u) =\) 2. \(\cos(2u) =\) 3. \(\tan(2u) =\) **Explanation:**Using double-angle formulas, we can find these trigonometric functions easily:- **Double-Angle Formula for Sine:** \[ \sin(2u) = 2 \sin(u) \cos(u) \]- **Double-Angle Formula for Cosine:** \[ \cos(2u) = \cos^2(u) - \sin^2(u) \]- **Double-Angle Formula for Tangent:** \[ \tan(2u) = \frac{2 \tan(u)}{1 - \tan^2(u)} \]**Note:** The condition \(\frac{\pi}{2} < u < \pi\) places \(u\) in the second quadrant where sine is positive and cosine is negative.

Name: **Objective:**Use the given conditions to find the exact values of \(
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Objective:**Use the given conditions to find the exact values of \(\sin(2u)\), \(\cos(2u)\), and \(\tan(2u)\) using the double-angle formulas.**Given:**\[\cos(u) = -\frac{15}{17}, \quad \frac{\pi}{2} < u < \pi\]**Expressions to Find:**1. \(\sin(2u