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- y = tan x is a trigonometric function that relates the angle x to the ratio of the opposite and adjacent sides of a right triangle. The graph of y = tan x is a periodic curve that has vertical asymptotes at x = (n + 1/2)π, where n is any integer. The derivative of y = tan x is y' = sec^2 x, which can be proved by using the chain rule and the identity cot x = 1 / tan x1. The solutions of y = tan x = √3 are x = 60°, 240°, 420° and 600°, obtained by adding 180° to the first solution2.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.We will prove the differentiation of tan x formula by chain rule. For this let us note that we can write y = tan x as y = 1 / (cot x) = (cot x) -1.www.cuemath.com/calculus/derivative-of-tan-x/The period of the graph (y = tan {x}) is 180° so to calculate the other solutions add 180°. (x) = 60°, 240°, 420° and 600°.www.bbc.co.uk/bitesize/guides/ztj6y4j/revision/6
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