2 – 2 cos 2.x 8. sec x csc x cot x + tanx - sin 2.x

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Prove identity. by choosing one side and manipulate until you arrive at other side. 

The equation displayed is:

\[ 
8. \quad \frac{2 - 2\cos 2x}{\sin 2x} = \sec x \csc x - \cot x + \tan x 
\]

### Explanation:

- **Left Side:**
  - The numerator is \(2 - 2\cos 2x\).
  - The denominator is \(\sin 2x\).

- **Right Side:**
  - \(\sec x \csc x\) is the product of the secant and cosecant functions.
  - \(- \cot x\) is the negative cotangent function.
  - \(+ \tan x\) is the tangent function.

### Additional Notes:

This expression likely involves simplifying or proving the equivalence of trigonometric identities. The left side appears to be a trigonometric fraction, which might be reduced or transformed using identities such as angle double formulas or Pythagorean identities. On the right side, the expression is a combination of different trigonometric functions which might also be simplified or proven by trigonometric identities.
Transcribed Image Text:The equation displayed is: \[ 8. \quad \frac{2 - 2\cos 2x}{\sin 2x} = \sec x \csc x - \cot x + \tan x \] ### Explanation: - **Left Side:** - The numerator is \(2 - 2\cos 2x\). - The denominator is \(\sin 2x\). - **Right Side:** - \(\sec x \csc x\) is the product of the secant and cosecant functions. - \(- \cot x\) is the negative cotangent function. - \(+ \tan x\) is the tangent function. ### Additional Notes: This expression likely involves simplifying or proving the equivalence of trigonometric identities. The left side appears to be a trigonometric fraction, which might be reduced or transformed using identities such as angle double formulas or Pythagorean identities. On the right side, the expression is a combination of different trigonometric functions which might also be simplified or proven by trigonometric identities.
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