If $\alpha = \frac{\pi }{4}$   then $sin2\alpha = \_\_\_\_\_\_.$

$\cos e{c}^{-1} x + se{c}^{-1} x = \_\_\_\_\_\_\_$   , where $\left|x\right| > 1$

${\sin }^2 43° + {\sin }^2 47° - {\tan }^2 45° = \_\_\_\_\_.$

$\cos 15° \sin 75° + \cos 75° \sin 15° = \_\_\_\_\_\_\_.$

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

$\sin \left(-x\right) = \_\_\_\_\_\_.$

$\tan \left(225°\right) = \_\_\_\_\_\_.$

The range of sin function is $\_\_\_\_\_\_.$

Principal period of $\tan \left(2x + 3\right) = \_\_\_\_\_\_.$

Value of $sin{18}^{\circ } = \_\_\_\_\_\_.$