Question

Trigonometry !!!
How did root 5 /3 came as sin alpha​

Answer 1

$good \: \: \: morning \\ \\ \\ \\ \\ \cos( \alpha ) = 2 \div 3 \\ \\ \sin( \alpha ) = \sqrt{1 - 4 \div 9} = \sqrt{5} \div 3 \\ \\ \\ becoz \: \: \: \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1 \\ \\ \sin( \alpha ) = \sqrt{1 - \cos {}^{2} ( \alpha ) } \\ \\ \\ \\ \\ similarly \: \\ \\ \\ \cos( \beta ) = \sqrt{15} \div 4 \\ \\ \\ \\ so \: \: \: \: \cos( \alpha - \beta ) = \cos( \alpha ) \times \cos( \beta ) + \sin( \alpha ) \times \sin( \beta ) \\ \\ \\ \\ \cos( \alpha - \beta ) = (2 \times \sqrt{15}) \div 6 + ( \sqrt{5 } \times 1) \div 16$