Principal period of $2 \sin x \cos x$ is $\_\_\_\_\_\_\_\_\_.$

$\cos \left(A-B\right) + \cos \left(2A+B\right) = \_\_\_\_\_\_\_\_.$

${\sin }^2 37\frac{1}{2} - {\sin }^2 7\frac{1}{2} = \_\_\_\_\_\_\_\_.$

If $\tan \theta = \frac{3}{4 }$ and $180° < \theta < 270°$ then $sec \theta = \_\_\_\_\_\_\_.$

${\sin }^2 A - {\cos }^2 A = \_\_\_\_\_\_.$

$\sin \frac{\pi }{ 6 } · \sin \frac{\pi }{ 4 } · \sin \frac{\pi }{ 3 } · \sin \frac{\pi }{ 2 } · \sin \mathrm{\pi } = \_\_\_\_\_\_\_.$

$se{c}^{-1} \left(-\sqrt{2}\right) = \_\_\_\_\_\_.$

$\cos \left(\frac{\pi }{2} + {\sin }^{-1} \frac{4}{5}\right) = \_\_\_\_\_\_\_\_.$

$\frac{4\pi }{9} = \_\_\_\_\_\_\_\_$ degree.

For $∆ABC , \sin \left(B + C\right) = \_\_\_\_\_\_\_\_.$