What is the value of $\frac{1}{2}$?

The value of $\int\limits_0^{\frac{\pi }{{2\omega }}} {5\,\sin \omega t} \,dt$ is

If $\tan \theta = \frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant,the value of $\cos \theta$ is

Which of the following relation$(s)$ is/are correct?
$(A)\ \sin (90^{\circ}+\theta)=\cos (-\theta)$
$(B)\ \sin (180^{\circ}-\theta)=\cos (90^{\circ}-\theta)$
$(C)\ \sin (360^{\circ}-\theta)=\cos (360^{\circ}-\theta)$
$(D)\ \sin (180^{\circ}+\theta)=\cos (90^{\circ}-\theta)$

$\int\limits_0^{\frac{\pi }{4}} {\sin 2x} \,dx$ is equal to

$\int \frac{3}{(2-x)^2} \, dx$ is equal to $:-$