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Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank. A. tan(sin-¹(x/2)) B. cos(sin-¹(x/2)) C. (1/2) sin(2 sin-¹(x/2)) D. sin(tan-¹(x/2)) E. cos (tan-¹(x/2)) 1. 2. 3. X √4-x² 2 √4+x² X 4. V4 x² 4 5. √4+x² x √4x² 2

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank. A. tan(sin-¹(x/2)) B. cos(sin-¹(x/2)) C. (1/2) sin(2 sin-¹(x/2)) D. sin(tan-¹(x/2)) E. cos (tan-¹(x/2)) 1. 2. 3. X √4-x² 2 √4+x² X 4. V4 x² 4 5. √4+x² x √4x² 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Trigonometric Expression Matching Exercise **Instructions:** Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the list provided. Enter the appropriate letter (A, B, C, D, or E) in each blank. **Trigonometric Expressions:** - A. \(\tan(\sin^{-1}(x/2))\) - B. \(\cos(\sin^{-1}(x/2))\) - C. \((1/2) \sin(2 \sin^{-1}(x/2))\) - D. \(\sin(\tan^{-1}(x/2))\) - E. \(\cos(\tan^{-1}(x/2))\) **Non-Trigonometric Functions:** 1. \(\frac{x}{\sqrt{4 + x^2}}\) 2. \(\frac{\sqrt{4 - x^2}}{x}\) 3. \(\sqrt{\frac{4}{4 + x^2}}\) 4. \(\frac{x\sqrt{4 + x^2}}{4}\) 5. \(\frac{\sqrt{4 - x^2}}{2}\) **Objective:** Determine the correct match between the trigonometric expression and the non-trigonometric function. Use your knowledge of inverse trigonometric identities and properties to find the correct pairings.
Transcribed Image Text:### Trigonometric Expression Matching Exercise **Instructions:** Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the list provided. Enter the appropriate letter (A, B, C, D, or E) in each blank. **Trigonometric Expressions:** - A. \(\tan(\sin^{-1}(x/2))\) - B. \(\cos(\sin^{-1}(x/2))\) - C. \((1/2) \sin(2 \sin^{-1}(x/2))\) - D. \(\sin(\tan^{-1}(x/2))\) - E. \(\cos(\tan^{-1}(x/2))\) **Non-Trigonometric Functions:** 1. \(\frac{x}{\sqrt{4 + x^2}}\) 2. \(\frac{\sqrt{4 - x^2}}{x}\) 3. \(\sqrt{\frac{4}{4 + x^2}}\) 4. \(\frac{x\sqrt{4 + x^2}}{4}\) 5. \(\frac{\sqrt{4 - x^2}}{2}\) **Objective:** Determine the correct match between the trigonometric expression and the non-trigonometric function. Use your knowledge of inverse trigonometric identities and properties to find the correct pairings.
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