Question

$\sqrt{4 + \sqrt{8 + 16 \csc { \alpha }^{4} \sin( { \alpha }^{4 } ) } }$
find the value​

Answer 1

$\sqrt{ 4 + \sqrt{8 + 16 \csc( { \alpha }^{4}) \sin( { \alpha }^{4} ) } } \\ = \sqrt{ 4 + \sqrt{8 + 16 \times \frac{1}{ \sin( { \alpha }^{4} ) } \times \sin( { \alpha }^{4} ) } } \\ = \sqrt{4 + \sqrt{8 + 1} } \\ = \sqrt{4 + \sqrt{9} } \\ = \sqrt{4 + 3} \\ = \sqrt{7} \\ = 2.64575 \: (approximately)$