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

8-94.

Use the sum and difference formulas to show that $\tan(\frac { \pi } { 2 }− θ) = \cot(θ)$ .

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

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

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

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

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