Chapter 6, Problem 30RE

To determine

Exact value of given expression.

Answer to Problem 30RE

  $-1$

Explanation of Solution

Given information:

  $\cot {200}^{°}\cot \left(-{70}^{°}\right)$

Formula used:

  $\begin{array}{l}\cot \left(n{180}^{°}+\theta \right)=\cot \theta \\ \cot \left(-\theta \right)=-\cot \theta \\ \cot \theta =\frac{1}{\tan \theta }\\ \tan \left({90}^{°}-\theta \right)=\cot \theta \end{array}$

  $\begin{array}{l}\cot {200}^{°}\cot \left(-{70}^{°}\right)\\ =\cot \left({180}^{°}+{20}^{°}\right)\left(-\cot \left({70}^{°}\right)\right)\\ =-\cot {20}^{°}\frac{1}{\tan {70}^{°}}\\ =-\frac{\cot {20}^{°}}{\tan \left({90}^{°}-{20}^{°}\right)}\end{array}$

  $\begin{array}{l}=-\frac{\cot {20}^{°}}{\cot {20}^{°}}\\ =\boxed{-1}\end{array}$