Question

The number of solutions of the equation tan2x · tanx = 1, x ∈ [0, 2π] is 4 5 6 7

Answer 1

Given : tan2x · tanx = 1, x ∈ [0, 2π]  

To find  :  number of solutions of the equation

Solution:

tan2x · tanx = 1,

tan2x  = 2Tanx/(1 - Tan²x)

=> ( 2Tanx/(1 - Tan²x)) ·Tanx = 1,

=> 2Tan²x = 1 - Tan²x

=>  3Tan²x = 1

=> Tan²x = 1/3

=> Tanx = ±1/√3

=> x = nπ ± π/6

x ∈ [0, 2π]

=> x  = π/6  , 5π/6  ,  7π/6 , 11π/6

Hence 4 Solutions

4 number of solutions of the equation tan2x · tanx = 1,  

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