### Home > PC > Chapter 8 > Lesson 8.2.2 > Problem8-94

8-94.

Use the sum and difference formulas to show that tan( θ) = cot(θ). Homework Help ✎

$\text{Convert: tan}\left(\frac{\pi}{2}-\theta\right)\text{ to }\frac{\text{sin}\left(\frac{\pi}{2}-\theta\right)}{\text{cos}\left(\frac{\pi}{2}-\theta\right)}.$

$\text{cot}\theta\text{ to }\frac{\text{cos}\theta}{\text{sin}\theta}$

$\frac{\text{sin}\left(\frac{\pi}{2}\right)\text{cos}\theta-\text{cos}\left(\frac{\pi}{2}\right)\text{sin}\theta}{\text{cos}\left(\frac{\pi}{2}\right)\text{cos}\theta+\text{sin}\left(\frac{\pi}{2}\right)\text{sin}\theta}=\frac{\text{cos}\theta}{\text{sin}\theta}$

$\text{Substitute the following known values: }\text{sin}\left(\frac{\pi}{2}\right)=1\text{cos}\left(\frac{\pi}{2}\right)=0$

$\frac{(1)\text{cos}\theta-(0)\text{sin}\theta}{(0)\text{cos}\theta+(1)\text{sin}\theta}=\frac{\text{cos}\theta}{\text{sin}\theta}\text{ Simplify further.}$