Question

$\frac{1}{\sec \theta }=$ _____ for an acute angle $\theta$ in a right angled triangle.

• A. $\cos \theta$
• B. $\sin \theta$
• C. $\tan \theta$
• D. None of these

Answer 1

The correct option is A $\cos \theta$

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

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

$\text{sec}\theta =\frac{hypotenuse}{adjacent}$

$\frac{1}{\text{sec}\theta }=\frac{1}{\frac{hypotenuse}{adjacent}}=\frac{adjacent}{hypotenuse}=\cos \theta$

$\therefore \frac{1}{\text{sec}\theta }=\cos \theta$