Question

if a+b=90 and sin a=1/3 then find the value of sin b​

Answer 1

given that

sinx = 1/3

and

x + y = 90°

x = 90° - y

sinx = sin(90° - y)

1/3 = cosy

cos²y = 1/9

${sin}^{2} y + {cos}^{2} y = 1 \\ {sin}^{2} y = 1 - {cos}^{2} y \\ {sin}^{2} y = 1 - \frac{1}{9} = \frac{9 - 1}{9} = \frac{8}{9} \\ \\ taking \: square \: roots \: on \: both \: sides \\ \\ siny = \frac{2 \sqrt{2} }{3}$