Locate the discontinuities of the function y=ln (tan^2 (x))

Since tan^2 (x) >0 for all x, there is no need to worry about any negative under the natural logarithm function. When tan^2 (x) = 0 and tan^2 (x) is undefined Since tan^2 (x) = sin^2 (x) / cos^2 (x), we see that any problem will result when either the numerator (tan^2 (x) = 0) or denominator equals zero (sin^2 (x) = 0 or cos^2 (x) = 0) Solve the two equations gives: sin (x) = 0 = = > x=πk for integer k cos (x) = 0 = = > x=π/2 + / - 2πk and x=3π/2 + / - 2πk integer k Combing all three gives discontinuities at x = + / - πk/2 for all integers k