Solve the equation 4*tan^2x - 1 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The trigonometric equation 4*tan^2x - 1 = 0 has to be solved.

4*tan^2x - 1 = 0

=> 4*tan^2x = 1

=> tan^2x = 1/4

=> tan x = 1/2 and tan x = -1/2

=> `x = tan^-1(1/2)` and `x = tan^-1(-1/2)`

=> x = 26 .56 + n*180 degrees and x = -26.56 + n*180 degrees

The solution of the equation `4*tan^2x - 1 = 0` is `+-26.56 + n*180` degrees where n is an integer.

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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We have to solve the equation 4*tan^2x - 1 = 0 for x.

4*tan^2x - 1 = 0

4*tan^2x = 1

tan^2x = 1/4

tan x = + 1/2 and tan x = -1/2

x = `tan^-1(1/2)` and x = `tan^-1(-1/2)`

The tan function is periodic and values of x separated by `pi` radians have the same value of tan x.

The solution of equation is `tan^-1(1/2) + n*pi` and `-tan^-1(1/2) + n*pi`

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