Question

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

• A. $\cot \theta$
• B. $\sin \theta$
• C. $\cos \theta$
• D. $\tan \theta$

Answer 1

Answer: (A)

$\cot \theta$

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

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

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

$=\frac{adjacent}{opposite}\times \frac{hypotenuse}{hypotenuse}$

$=\frac{adjacent}{opposite}$

$=\cot \theta$

Hence, $\frac{\cos \theta }{\sin \theta }=\cot \theta$.