Question

find the number of solutions of the equation 2 tan^-1 (tan x) = 6-x

Answer 1

$HEYA \:$

2 × Tan-¹(Tan x ) = 6 - x

2x = 6 - x

Becoz Tan-¹(Tan x) = x : x€R

3x = 6

x = 2

So, the number of solutions For given Equation is 2

Answer 2

The given equation  2 tan^-1 (tan x) = 6 -x  has three solution.

Given:

2 tan^-1 (tan x) = 6-x

To Find:

The number of solutions to the given equation

Solution:

2 tan^-1 (tan x) = 6-x = y

tan^-1 (tan x) = y  and

(6-x)/2 = y ⇒ x+2y-6 =0

To find the number of solutions to the given equation, We plot the graph of

tan^-1 (tan x) = y  and  x+2y-6 =0.

From the graph below, both the equation intersect at only three points.

Therefore, the given equation  2 tan^-1 (tan x) = 6 -x  has three solution.

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