Solve for -pi < x < pi: tanx = 4cotx + 3

tanx = 4cotx + 3  - Multiply through by tan to form a quadratic. tan^2x = 4 + 3tanx - Simplify by allowing y to equal tanx. y^2 = 4 + 3y - Rearange to standard quadratic form. y^2 - 3y -4 = 0 - Factorise. (y - 4)(y + 1) = 0 Therefore y = 4 and y = -1 Substitute y=tanx to solve for x: y = 4 tanx = 4 x = tan^-14 x= 1.326 (3d.p.) tanx = -1 x = tan^-1 -1 x = -pi/4