ctg 15 - tg 15 = cos15/sin15 - sin15/cos15 = (cos^2 15 - sin^2 15)/(sin15 * cos15) = cos30/sin15*cos15 = sqrt(3)/(2sin15 * cos15) = sqrt(3)/ sin30 = sqrt(3)/ 1/2 = 2sqrt(3)
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ctg 15 - tg 15 = cos15/sin15 - sin15/cos15 = (cos^2 15 - sin^2 15)/(sin15 * cos15) = cos30/sin15*cos15 = sqrt(3)/(2sin15 * cos15) = sqrt(3)/ sin30 = sqrt(3)/ 1/2 = 2sqrt(3)