Question

Solve the equation$cot\left(2\theta \right)=1,\mathrm{where}0°<\theta <90°$

Short answer

The value is$\theta =22.5°$

Step-by-step solution

Step 1. Given Information

The given equation is$cot\left(2\theta \right)=1$

Step 2. Calculation

Solve the given equation to find the value,

$$\begin{gathered} cot\left(2\theta \right)=1 \\ cot\left(2\theta \right)=\mathrm{co}t\left(\frac{\mathrm{\pi }}{4}\right) \\ 2\theta =\frac{\mathrm{\pi }}{4} \\ \mathrm{\theta }=\frac{\mathrm{\pi }}{8} \\ \theta =\frac{180}{8} \\ \theta =22.5° \end{gathered}$$

The value of theta lies in the range specified by the interval $\left(0,90°\right)$.

Thus, the value of$\theta =22.5°$