please help me with this. ## Trigonometric Identity Proof**Objective:**Prove the following trigonometric identity:\[ \frac{\cot A + \tan A}{\cot A - \tan A} = \sec 2A \]**Proof:**We'll start by using the definitions and identities of trigonometric functions to derive the result.1. **Definition and Identities:** \[ \cot A = \frac{\cos A}{\sin A} \] \[ \tan A = \frac{\sin A}{\cos A} \]2. **Substitute these into the given equation:** \[ \frac{\frac{\cos A}{\sin A} + \frac{\sin A}{\cos A}}{\frac{\cos A}{\sin A} - \frac{\sin A}{\cos A}} \]3. **Combine the fractions in the numerator and denominator:** \[ \frac{\frac{\cos^2 A + \sin^2 A}{\sin A \cos A}}{\frac{\cos^2 A - \sin^2 A}{\sin A \cos A}} \]4. **Simplify the fraction by multiplying numerator and denominator by \(\sin A \cos A\):** \[ \frac{\cos^2 A + \sin^2 A}{\cos^2 A - \sin^2 A} \]5. **Use the Pythagorean identity (\(\cos^2 A + \sin^2 A = 1\)) in the numerator:** \[ \frac{1}{\cos^2 A - \sin^2 A} \]6. **Express the denominator using the double-angle identity (\(\cos 2A = \cos^2 A - \sin^2 A\)):** \[ \frac{1}{\cos 2A} \]7. **Recognize that \(\frac{1}{\cos 2A}\) is the definition of \(\sec 2A\):** \[ \sec 2A \]Thus, we have proved that:\[\frac{\cot A + \tan A}{\cot A - \tan A} = \sec 2A\]This identity illustrates the relationship between cotangent, tangent

Name: please help me with this. ## Trigonometric Identity Proof**Objective:*
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: please help me with this. ## Trigonometric Identity Proof**Objective:**Prove the following trigonometric identity:\[ \frac{\cot A + \tan A}{\cot A - \tan A} = \sec 2A \]**Proof:**We'll start by using the definitions and identities of trigonometric fu