Question

If in a triangle (ABC) ; angle C=90°.Then find the equation whose roots are tan(alpha) and tan(bita)​

Answer 1

Are those tanA and tanB??

If so,

tanA = a/c

tan B= b/c

so the equation whose roots are tanA and tan B are

${x}^{2} - ( \tan(a) + \tan(b)) x + \tan(a) \tan(b) = 0 \\ = > {x}^{2} - ( \frac{a}{c} + \frac{b}{c})x + \frac{ab}{ {c}^{2} } = 0 \\ = > {c}^{2} {x}^{2} - (ac + bc)x + ab = 0$

Is the required equation