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
ZL
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