Question

Solve for x:

(i) tan^-1 (x + 1) + tan^-1 (x - 1) = tan^-1 18/31

(ii) sin^-1 x + sin^-1 2x = π/3

(iii) tan(cos^-1 x) = sin(cot^-1 (1/2))

(iv) cot^-1 x - cot^-1 (x + 2) = π/12, where x > 0 

Answer 1

(i) 1/4

(ii) (1/2) √(3/7)

(iii) ± √5/3

(iv) √3