Find the value of ${\cos }^2\alpha +{\sin }^2\theta$ if $\cos \theta =\frac{1}{2}$ and  $\alpha +\theta =\frac{\pi }{2}.$

Find the value of following equation:

${\left(\sec \varnothing -\tan \varnothing \right)}^2{\left(1+\sin \varnothing \right)}^2÷{\sin }^2 \varnothing =?$

If $3\sin \theta =2{\cos }^2\theta , 0^0<\theta <{90}^0$. Then the value of $({\tan }^2\theta +se{c}^2\theta -\cos e{c}^2\theta )$ is: