Let f x = m a x tan ⁡ x , cot ⁡ x . Then the number of roots of the equation f x = 1 2 in 0,2 π is

Question

Let f x = m a x tan ⁡ x , cot ⁡ x . Then the number of roots of the equation f x = 1 2 in 0,2 π is, 0, 1, 2, 4

MARKS App · Accepted Answer

From the graph of tan x and cot x , we see that the range of f x is - 1,0 ∪ 1 , ∞ . Hence, f x = m a x tan ⁡ x , cot ⁡ x and g x = 1 2 do not cut each other ⇒ The number of solutions is zero.

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