Question

Find the exact value of the expression-

$\tan 20°-\frac{\cos 70°}{\cos 20°}$

Short answer

The required value is,

$\tan 20°-\frac{\cos 70°}{\cos 20°}=$$0$

Step-by-step solution

Step 1. Given information

Given expression,

$\tan 20°-\frac{\cos 70°}{\cos 20°}$

Step 2. Calculation

Solving the given expression,

$$\begin{gathered} \tan 20°-\frac{\cos 70°}{\cos 20°} \\ =\frac{\sin 20°}{\cos 20°}-\frac{\cos 70°}{\cos 20°} \end{gathered}$$ ----------$\left(\tan \theta =\frac{\sin \theta }{\cos \theta }\right)$

$$\begin{gathered} =\frac{\sin 20°-\cos 70°}{\cos 20°} \\ =\frac{\sin (90°-70)-\cos 70°}{\cos 20°} \\ =\frac{\cos 70°-\cos 70°}{\cos 20°} \\ =0 \end{gathered}$$ -----------$\left\{\sin \left(90°-\theta \right)=\cos \theta \right\}$