Question

Find the exact value of the expression-

$cot40°-\frac{\sin 50°}{\sin 40°}$

Short answer

The required value is,

$cot40°-\frac{\sin 50°}{\sin 40°}=0$

Step-by-step solution

Step 1. Given information

Given expression,

$cot40°-\frac{\sin 50°}{\sin 40°}$

Step 2. Calculation

Solving the given expression,

$$\begin{gathered} cot40°-\frac{\sin 50°}{\sin 40°} \\ =\frac{\cos 40°}{\sin 40°}-\frac{\sin 50°}{\sin 40°} \end{gathered}$$ ---------$\left(cot\theta =\frac{\cos \theta }{\sin \theta }\right)$

$$\begin{gathered} =\frac{\cos 40°-\sin 50°}{\sin 40°} \\ =\frac{\cos (90°-50°)-\sin 50°}{\sin 40°} \\ =\frac{\sin 50°-\sin 50°}{\sin 40°} \\ =0 \end{gathered}$$ ----------$\left\{\cos \left(90°-\theta \right)=\sin \theta \right\}$