Question

.find sina
$\sin( \alpha ) + \sqrt{ \sin( \alpha ) + \sqrt{ \sin( \alpha ) + \sqrt{ \sin( \alpha ) } } }..... \infty = { \sec( \beta ) }^{4}$

Answer 1

Given that
$\sin( \alpha ) + \sqrt{ \sin( \alpha ) + \sqrt{ \sin( \alpha ) .....} } = { \sec ^{4} ( \beta ) } \\ \sin( \alpha ) + \sqrt{ \sec {}^{4} ( \beta ) } = \sec {}^{4} ( \beta ) \\ \sin( \alpha ) + \sec {}^{2} ( \beta ) = \sec {}^{4} ( \beta ) \\ \sin( \alpha ) = \sec {}^{2} ( \beta ) ( \sec {}^{2} ( \beta ) - 1) \\ \sin( \alpha ) = \sec {}^{2} ( \beta ) \times \tan {}^{2} ( \beta )$