(i) Show that tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/3 + tan^-1 1/8 = π/4

Question

(i) Show that tan⁻¹ \(\frac{1}{5}\) + tan⁻¹\(\frac{1}{7}\) + tan⁻¹\(\frac{1}{3}\) + tan⁻¹\(\frac{1}{8}\) = \(\frac{π}{4}\)

(ii) Given that Cot 3θ = \(\frac{3cot^2 θ -1}{cot^3 θ - 3cot θ'}\)

cot^-1 \(\frac{3x^2 θ -1}{x^3 θ - 3x θ'}\) , |x|<√3 is 3cot¹ x

Answer 1

(ii) Put x = cot θ ⇒ θ = cot^-1x

= Cot ^-1 [cot 3θ] = 3θ = 3cot^-1x