Question

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\tan {10}^{\mathrm{o}}\cot {10}^{\mathrm{o}}$

Short answer

The exact value of the expression is$1.$

Step-by-step solution

Step 1. Given Information

Given that the trigonometric expression is $\tan {10}^{\mathrm{o}}\cot {10}^{\mathrm{o}}.$To find the exact value of the expression using identity.

Step 2. Fundamental identity

On using the fundamental identity,

$$\begin{gathered} \mathrm{cot\theta }=\frac{1}{\mathrm{tan\theta }} \\ \tan {10}^{\mathrm{o}}\cot {10}^{\mathrm{o}}=\tan {10}^{\mathrm{o}}\frac{1}{\tan {10}^{\mathrm{o}}} \\ \tan {10}^{\mathrm{o}}\cot {10}^{\mathrm{o}}=1 \end{gathered}$$