Question

Find the exact value of the expression-

$\frac{\cos 40°}{\sin 50°}$

Short answer

The required value is,

$\frac{\cos 40°}{\sin 50°}=1$

Step-by-step solution

Step 1. Given information

Given expression

$\frac{\cos 40°}{\sin 50°}$

Step 2. Calculation

Solving the given expression,

$$\begin{gathered} \frac{\cos 40°}{\sin 50°}=\frac{\cos (90°-50°)}{\sin 50°} \\ =\frac{\sin 50°}{\sin 50°} \\ =1 \end{gathered}$$ ----------(complementary angle,$\cos (90°-\theta )=\sin \theta$)