Relation among Trigonometric Ratios

Q.

Which of the following options is equal to $\frac{\sin \theta +1-\cos \theta }{\cos \theta -1+\sin \theta }?$

1. $\frac{\cos \theta }{1-\sin \theta }$

2. $\frac{1+\sin \theta }{\cos \theta }$

3. $\frac{1+\sin \theta }{1-\sin \theta }$

4. $\tan \theta +\sec \theta$

Q. $\frac{sin{18}^{\circ }}{cos{72}^{\circ }}=$

Q. Evaluate :
$\frac{sin{18}^{\circ }}{cos{72}^{\circ }}$_
[1 Mark]

Q.

If $\sec 3\beta =cosec\left(\beta -22°\right)$ and $3\beta$ is an acute angle, find the value of $\beta$.

Q.

If $\sec 2\beta =cosec\left(\beta -24°\right)$ and $2\beta$ is an acute angle, find the value of $\beta .$

Q.

sec (60° + A) - cosec (30° - A) = ___.

1. 1

2. 0

3. -1

4. -2