Question

if sin A=3/5,find the value of 2 cot^2A-3​

Answer 1

$sina = \frac{3}{5} \\ \\ cosa = \sqrt{1 - {sin}^{2} a} \\ cosa = \sqrt{1 - \frac{9}{25} } \\ cosa = \sqrt{ \frac{16}{25} } \\ cosa = \frac{4}{5} \\ \\ \frac{cosa}{sina} = cota = \frac{4}{3} \\ \\ 2 {cot}^{2} a - 3 = 2( { \frac{4}{3} })^{2} - 3 \\ = 2 \times \frac{16}{9} - 3 \\ = \frac{32 - 27}{9} \\ = \frac{5}{9}$