Verify identity **Title: Verifying Trigonometric Identity using Algebraic Methods****Objective:**The goal of this exercise is to verify a given trigonometric identity using algebraic manipulations and possibly a graphing utility to check your work.**Identity to Verify:**\[\frac{3 \cos(x) - \frac{3 \cos(x)}{1 - \tan(x)}}{\sin(x) - \cos(x)} = \frac{3 \sin(x) \cos(x)}{\sin(x) - \cos(x)}\]**Steps to Verify:**1. **Initial Expression:** \[ 3 \cos(x) - \frac{3 \cos(x)}{1 - \tan(x)} \]2. **Factor and Rearrange:** \[ = (3 \cos(x)) \left(1 - \frac{1}{1 - \tan(x)}\right) \]3. **Substitute and Simplify:** \[ = (-3 \cos(x)) \left(\frac{1 - \tan(x) - 1}{1 - \tan(x)}\right) \] 4. **Simplify Further:** \[ = (-3 \cos(x)) \left(\frac{-\tan(x)}{1 - \tan(x)}\right) \] 5. **Factor and Simplify:** \[ = (-3 \cos(x)) \left(\frac{\tan(x)}{1 - \tan(x)}\right) \]6. **Final Expression:** \[ = \frac{3 \sin(x) \cos(x)}{\sin(x) - \cos(x)} \]**Conclusion:**By following these algebraic steps, the original expression has been successfully transformed and verified as equivalent to the target identity on the right-hand side.**Additional Resources:**If additional help is needed, utilize the "Need Help?" section where resources such as reading materials ("Read It") or instructional videos ("Watch It") are available.**Note:**Utilizing a graphing calculator or software with a table feature can provide a visual confirmation that the two expressions are equivalent by comparing output values for various inputs of \(x\).

Name: Verify identity **Title: Verifying Trigonometric Identity using Algebr
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Verify identity **Title: Verifying Trigonometric Identity using Algebraic Methods****Objective:**The goal of this exercise is to verify a given trigonometric identity using algebraic manipulations and possibly a graphing utility to check your work.**