Simplifying Trig Expressions Worksheet with Answer Key

What's on the worksheet

1. Simplify each expression to a single trigonometric function, a power of one, or a number.
   \dfrac{\sec^2 x - 1}{\sec^2 x}\cot x\,(\sec x - \cos x)\tan x\,(\csc^2 x - 1)\dfrac{\tan x + \cot x}{\sec x}\dfrac{\sec x}{1 + \tan^2 x}
2. Use the even and odd properties and the cofunction identities to simplify each expression.
   \cot\left(\dfrac{\pi}{2} - x\right)\cos(-x)\csc(-x)\dfrac{1 - \sin^2(-x)}{\cos\left(\frac{\pi}{2} - x\right)}\tan(-x)\sin\left(\dfrac{\pi}{2} - x\right) + \sin x
3. Simplify x x + x to a single trigonometric function.
4. Simplify x x - x to a single trigonometric function.
5. Simplify ² x - 3 x + 1 x - 1.
6. For x > 5, substitute x = 5θ, with 0 < θ < π2, into x√(x² - 25).