Question

Prove that tan^1(m/n)-tan^1(m-n)/(m+n)=pi /4

Answer 1

$\textbf{Answer :}$

Now,

L.H.S. = tan⁻¹ (m/n) - tan⁻¹ {(m - n)/(m + n)}

= tan⁻¹ [{(m/n) - (m - n)/(m + n)}/{1 + (m/n)(m - n)/(m + n)}]

= tan⁻¹ [{m (m + n) - n (m - n)}/{n (m + n) + m (m - n)}]

= tan⁻¹ [(m^2 + mn - mn + n^2)/(mn + n^2 + m^2 - mn)]

= tan⁻¹ (1)

= π/4

= R.H.S. [Proved]

#$\textbf{MarkAsBrainliest}$

Answer 2

Refer the attachment