Question

Please help me out with this question

Answer 1

Proof :

Given that,

tanα = m/(m + 1), tanβ = 1/(2m + 1)

Now, tan(α + β)

= $\frac{tan\alpha+tan\beta}{1-tan\alpha\:tan\beta}$

= $\frac{\frac{m}{m+1}+\frac{1}{2m+1}}{1-\frac{m}{m+1}\frac{1}{2m+1}}$

= $\frac{m(2m+1)+(m+1)}{(m+1)(2m+1)-m}$

= $\frac{2m^{2}+2m+1}{2m^{2}+2m+1}$

= 1

= tan(π/4)

i.e., α + β = π/4 (proved)