Question

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

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

Answer 1

The correct option is A $\sin \theta$

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

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

$\text{cosec}\theta =\frac{hypotenuse}{opposite}$

$\frac{1}{\text{cosec}\theta }=\frac{1}{\frac{hypotenuse}{opposite}}=\frac{opposite}{hypotenuse}=\sin \theta$

$\therefore \frac{1}{\text{cosec}\theta }=\sin \theta$