Show that tan(x) + cot(x) = 2cosec(2x)

For this we have to use trignometric identities, e.g Tan(x)= sin(x)/cos(x), sin²(x) + cos²(x) = 1, 1/sin(x) = cosec(x)
tan(x) + cot(x) = sin(x)/cos(x) + cos(x)/sin(x) = [sin²(x) + cos²(x)]/sin(x)cos(x) = 1/sin(x)cos(x) ------------------------> Sin(2x) = 2sin(x)cos(x) so sin(x)cos(x) = Sin(2x)/2 = 2/sin(2x) = 2cosec(2x)