### Home > CALC > Chapter 1 > Lesson 1.3.2 > Problem1-116

1-116.

Calculus problems often require using one or more of the trigonometric identities to solve problems. Solve each of the following equations where $x ∈ [0, 2π]$. Use exact values.

1. $\text{tan } x · \text{csc }x = 2$

Simplify the left side of the equation to solve for $x$.
Remember that $\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$ and $\text{csc}x=\frac{1}{\text{sin}x}$.

$\frac{\text{sin}x}{\text{cos}x}\cdot\frac{1}{\text{sin}x}=2$
$\frac{1}{\text{cos}x}=2$
$\text{cos}x=\frac{1}{2}$

Use the unit circle to solve for $x$.

$\frac{\pi }{3},\ \frac{5\pi }{3}$

1. $\operatorname { sin } x \cdot \operatorname { cos } x = \frac { 1 } { 4 }$

See part (a).

1. $2 \text{ sin}^2 x -\text{cos }x - 1 = 0$

See part (a).

1. $\text{tan }x +\text{cot }x = -2$

See part (a).