Trigonometric identities Knowledge-Based Download PDF

Questions

1. 1.

   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) $1 + \sin x$
   • C) $\cos x + \sin x$
   • D) $\tan x + 1$
2. 2.

   Which of the following is equivalent to the expression $\frac{\cos^4 x - \sin^4 x}{1 - \tan^2 x}$ for all values of $x$ where it is defined?

   • A) $\cos^2 x$
   • B) $\sin^2 x$
   • C) $\sec^2 x$
   • D) 1
3. 3.

   Simplify the trigonometric expression $\frac{\tan x}{\sec x - 1} + \frac{\tan x}{\sec x + 1}$ for all values of $x$ where it is defined.

   • A) $2\csc x$
   • B) $2\sec x$
   • C) $2\tan x$
   • D) $2\cot x$
4. 4.

   Which of the following is equivalent to the expression $\frac{\sec x - \cos x}{\tan x}$ for all values of $x$ for which it is defined?

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

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

   • A) $2\csc\theta$
   • B) $2\sec\theta$
   • C) $2\tan\theta$
   • D) $2\sin\theta$