Question 1 :
If $\displaystyle \theta =45$ then $\displaystyle \frac { 2\tan { \theta  }  }{ 1+{ \tan }^{ 2 }\theta  } $ is :

Question 4 :
Given that $\sin\alpha = \displaystyle\frac{1}{2}$ and $\cos\beta=\displaystyle\frac{1}{2}$, then the value of $(\alpha + \beta)$ is

Question 5 :
In $\triangle ABC,   \angle B=90^o,   \angle A=30^o,   AB =9  cm\ $, then $BC =$

Question 8 :
Evaluate the following<br><br>$(i)\quad \displaystyle\frac{1+\tan^230^{\small\circ}}{1-\tan^230^{\small\circ}}+cosec^260^{\small\circ} - \cos^245^{\small\circ} + \sin^245^{\small\circ} + \displaystyle\frac{1+\cot^260^{\small\circ}}{1-\cot^260^{\small\circ}}$<br><br>$(ii)\quad 4(\sin^430^{\small\circ} + \cos^460^{\small\circ}) - 3(\cos^245^{\small\circ} - \sin^290^{\small\circ})$

Question 10 :
If $\displaystyle \cos A= \frac{1}{2}$ and $\displaystyle \sin B= \frac{1}{\sqrt{2}}$ , find the value of $\displaystyle \frac{\tan A\, -\, \tan B}{1\, +\, \tan A\tan B}$<br/><br/>

Question 11 :
The value of expression&#160;$\displaystyle \frac{\sin 30^{\circ}+\tan 45^{\circ}-\sec 60^{\circ}}{\text{cosec}30^{\circ}-\cot 45^{\circ}-\cos 60^{\circ}}$ =&#160;