Trigonometric identities Knowledge-Based Practice

Questions

1. 1.

   Which of the following is equivalent to the expression $\frac{1 - \cos(2x) + \sin(2x)}{1 + \cos(2x) + \sin(2x)}$ for all values of $x$ where the expression is defined?

   • A) $\cot(x)$
   • B) $\tan(x)$
   • C) $\sec(x)$
   • D) $\cos(x)$
2. 2.

   Which of the following is equivalent to the expression $\frac{1 - 2\sin^2(x)}{\cos(x) + \sin(x)}$ for all values of $x$ where the expression is defined?

   • A) $\cos(x) + \sin(x)$
   • B) $1 - \tan(x)$
   • C) $\sin(x) - \cos(x)$
   • D) $\cos(x) - \sin(x)$
3. 3.

   Which of the following is equivalent to the expression $\frac{\tan(x) + \cot(x)}{\sec^2(x)}$ for all values of $x$ where the expression is defined?

   • A) $\tan(x)$
   • B) $\sin(x)\cos(x)$
   • C) $\cot(x)$
   • D) $\sec(x)\csc(x)$
4. 4.

   Which of the following is equivalent to the expression $(\sec(x) - \tan(x))(\csc(x) + 1)$ for all values of $x$ where the expression is defined?

   • A) $\tan(x)$
   • B) $\cos(x)$
   • C) $\sec(x)$
   • D) $\cot(x)$
5. 5.

   Which of the following is equivalent to the expression $\frac{\sin(x)}{1 + \cos(x)} + \frac{1 + \cos(x)}{\sin(x)}$ for all values of $x$ where the expression is defined?

   • A) $2\sin(x)$
   • B) $2\cos(x)$
   • C) $2\csc(x)$
   • D) $2\sec(x)$

Answers and step-by-step solutions appear after you finish the test.