Question

For an acute angle $\theta$ in a right angled triangle, $\frac{1}{\tan \theta }=$

• A. $\text{cosec}\theta$
• B. $\sec \theta$
• C. $\cot \theta$
• D. None of these

Answer 1

The correct option is C $\cot \theta$

$\sin \theta =\frac{opposite}{hypotenuse}$

$\cos \theta =\frac{adjacent}{hypotenuse}$

$\frac{\sin \theta }{\cos \theta }=\frac{\frac{opposite}{hypotenuse}}{\frac{adjacent}{hypotenuse}}$

$=\frac{opposite}{adjacent}$

$=\tan \theta$

$\therefore \frac{\sin \theta }{\cos \theta }=\tan \theta$.

$\frac{1}{\tan \theta }=\frac{\cos \theta }{\sin \theta }=\frac{\frac{adjacent}{hypotenuse}}{\frac{opposite}{hypotenuse}}$

$=\frac{adjacent}{opposite}$

$=\cot \theta$

$\therefore \frac{1}{\tan \theta }=\cot \theta$