Question

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

• A. $\cos \theta$
• B. $\cot \theta$
• C. $\sec \theta$
• D. $\text{cosec}\theta$

Answer 1

Answer: (D)

$\text{cosec}\theta$

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

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

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

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