Simplifying a hard trigonometric expression: ACT Math Practice Question

Try this ACT math practice question that tests your ability to algebraically simplify a trigonometric expression using trigonometric identities.

$$\dfrac{\cos \theta}{1 – \sin \theta} \quad – \quad \dfrac{\sin \theta}{\cos \theta}$$

When $\cos \theta \neq 0$ and $\sin \theta \neq 1$, which of the following is equivalent to the expression above?

1. $\quad \sec \theta$
2. $\quad \csc \theta$
3. $\quad \cos \theta$
4. $\quad \cos^{2} \theta$
5. $\quad \dfrac{\cos \theta – \sin \theta}{(\cos \theta)(1 – \sin \theta)}$

Choice A

Video explanation