Question

Tanx=m\m+1,tana=1/2m+1 then tanx+a=

Answer 1

Answer:

$\tan(x) = \frac{m}{m + 1} \\ \tan(a) = \frac{1}{2m + 1} \\ \tan(x + a) = \frac{ \tan(x) + \tan(a) }{1 - \tan(x) \times \tan(a) } \\ = \frac{ \frac{m}{m + 1} + \frac{1}{2m + 1} }{1 - ( \frac{m}{m + 1})( \frac{1}{2m + 1}) } \\ = \frac{ \frac{m(2m + 1) + m + 1}{(m + 1)(2m + 1)} }{ \frac{(m + 1)(2m + 1) - m}{(m + 1)(2m + 1)} } \\ = \frac{2 {m}^{2} + m + m + 1 }{2 {m}^{2} + m + 2m + 1 - m } \\ = \frac{2 {m}^{2} + 2m + 1 }{2 {m}^{2} + 2m + 1 } \\ = 1$