10. no calculater way please **Trigonometric Identity Verification**Show that \( \tan(x) + \cot(x) = \sec(x) \csc(x) \). (Verify this identity.)**Verification:**To verify the trigonometric identity, we will transform both sides of the equation to make them equal.1. **Left Side:**\[ \tan(x) + \cot(x) \]We know that:\[ \tan(x) = \frac{\sin(x)}{\cos(x)} \]\[ \cot(x) = \frac{\cos(x)}{\sin(x)} \]Combining these, we get:\[ \tan(x) + \cot(x) = \frac{\sin(x)}{\cos(x)} + \frac{\cos(x)}{\sin(x)} \]To add these fractions, find a common denominator:\[ \tan(x) + \cot(x) = \frac{\sin^2(x) + \cos^2(x)}{\sin(x)\cos(x)} \]Using the Pythagorean identity \( \sin^2(x) + \cos^2(x) = 1 \):\[ \tan(x) + \cot(x) = \frac{1}{\sin(x)\cos(x)} \]2. **Right Side:**\[ \sec(x) \csc(x) \]We know that:\[ \sec(x) = \frac{1}{\cos(x)} \]\[ \csc(x) = \frac{1}{\sin(x)} \]Multiplying these, we get:\[ \sec(x) \csc(x) = \frac{1}{\cos(x)} \cdot \frac{1}{\sin(x)} = \frac{1}{\sin(x)\cos(x)} \]3. **Conclusion:**Since both the left side and the right side simplify to:\[ \frac{1}{\sin(x)\cos(x)} \]the identity is verified. Therefore,\[ \tan(x) + \cot(x) = \sec(x) \csc(x) \]is true.

The answer is given below: Remember 1) sin(x)cos(x)=tan(x)2)cos(x)sin(x)= cot(x)3) sin2(x) +…

Answered: Show that tan(x) + cot(x) = sec(x)…

Show that tan(x) + cot(x) = sec(x) csc(x). (Verify this identity.)

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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