Question

tan⁻¹(-tan13π/8) is.......,Select Proper option from the given options.
(a) - 5π/8
(b) 3π/8
(c) - 3π/8
(d) 13π/8

Answer 1

we have to find the value of tan^-1(-tan13π/8)

we know, tan^-1(-x) = -tan^-1(x)

so, tan^-1(-tan13π/8) = -tan^-1(tan13π/8)

= - tan^-1{tan(2π - 3π/8)}

we know, tan(2π - x) =- tanx

so, - tan^-1{tan(2π- 3π/8)} = -tan^-1{-tan(3π/8)}

= tan^-1(tan3π/8)

now it seems tan^-1(tanx) , which equals x when x belongs to -π/2 < x < π/2

so, tan^-1(tan3π/8) = 3π/8

hence, option (b) is correct.