Question

If tan^2A − 3tanA +2 = 0, then find all possible values of sinA

Answer 1

$tan {}^{2} a - 3tan \: a + 2 = 0$

$tan {}^{2} a - 3tan \: a = - 2$

$\frac{sin {}^{2}a }{cos {}^{2} a} - 3 (\frac{sin \: a}{cos \: a} ) = - 2$

$\frac{sin {}^{2}a - 3sin \: a \times cos \: a }{cos {}^{2}a } = - 2$

$sin \: a(sin \: a - 3cos \: a) = - 2cos {}^{2} a$