A Simple Trigonometric Problem.

Trigonometric equation can be solved using trigonometric identities and find the value of x/radian/degree

Topic : Trigonometric Equation

In Trigonometric functions - Sine, Cosine, tan's value are found as explained below.

Problem : Solve tan 2x = 3 tan x and find x in degrees

Solution :
tan 2x = 3 tan x
we have tan 2x = 2 tan x/1 - tan² x
2 tan x/1 - tan² x = 3 tan x
2 tan x = 3 tan x (1 - tan² x)
2 tan x = 3 tan x - 3 tan³ x
3 tan³ - 3 tan x + 2 tan x = 0
3 tan³ - tan x = 0
or tan x (3 tan² x - 1) = 0
tan x = 0 or 3 tan² - 1 = 0
x = 0 or tan² = 1/3
x = 0 or tan x = ± 1/√3
x = 0⁰
or
tan x = +1/√3 ; x = 30⁰ or x = 180⁰ + 30⁰ = 210⁰ and
if x = -1/√3 ; x = 180⁰ - 30⁰ = 150 or 360⁰ - 30⁰ = 330⁰

So x = 0⁰, 30⁰, 150⁰, 210⁰, 330⁰


If required values can be converted into radians.
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