$\sin \left(\frac{5 \pi}{3}\right) + \sec \left(\frac{13 \pi}{3}\right) = $

$\sin 15^\circ + \cos 105^\circ = $

If $\left[1-\cos \left(\frac{\pi}{2}+\alpha\right)+\sin \left(\frac{3 \pi}{2}+\alpha\right)\right]^2+\left[1-\sin \left(\frac{3 \pi}{2}-\alpha\right)-\cos \left(\frac{3 \pi}{2}+\alpha\right)\right]^2=a+b \sin ^2\left(\frac{\pi}{4}+\alpha\right)$,then $a^2+b^2=$

Find the value of $\operatorname{cosec} 750^{\circ} - 2 \cot 765^{\circ}$.

$\sin 690^{\circ} \times \sec 240^{\circ} = $

$\tan A = \frac{-60}{11}$ and $A$ does not lie in the $4^{\text{th}}$ quadrant. $\sec B = \frac{41}{9}$ and $B$ does not lie in the $1^{\text{st}}$ quadrant. If $\operatorname{cosec} A + \cot B = K$,then $24K =$