# (a) The principal value of tan^-1(-1) is [π/4 , -π/4, π-π/4, π+π/4]

9 views
ago
closed ago

(a) The principal value of tan-1(-1) is

(b) If tan -1 ($\frac{x-1}{x-2}$) + tan-1 ($\frac{x-1}{x+2}$) = $\frac{π}{4}$ then find the value of x

+1 vote
ago by (18.3k points)
selected ago by

(a) $-\frac{π}{4}$

⇒ $\frac{2x^2 - 4}{-3}$ = 1 ⇒ 2x2 - 4 = -3 ⇒ x = ±$\frac{1}{\sqrt2}$