If $sin 3\theta sec 2\theta$ = 1, then what is the value of $\left[3 tan^{2} \left(\frac{5\theta}{2}\right) - 1\right]$?
1). 0
2). 1
3). 2
4). 3
If $\theta$ is acute angle and $tan \theta - cot \theta$ = 0, then what is the value of $tan26 \theta + cot100 \theta$?
1). -2
2). 0
3). 1
4). 2
What is the value of $sin \left(-\frac{\pi}{3}\right) + cos\left(-\frac{\pi}{6}\right)$?
1). 0
2). 1
3). 2
4). 3
If sum of the areas of the circumcircle and the incircle of an equilateral triangle is 770 cm2, then what is the area (in cm2) of the triangle?
1). $125\sqrt{3}$
2). $147\sqrt{3}$
3). $156\sqrt{3}$
4). $169\sqrt{3}$
If an equilateral triangle has side 12 cm, then what is the difference (in cm) between the circumradius and inradius?
1). $2\sqrt{2}$
2). $3\sqrt{2}$
3). $2\sqrt{3}$
4). $3\sqrt{3}$