Solve tan2x + 4x = 2(1+2x) ?

Question

find all solutions in the interval 0<x<360 degrees

thnx!!!

Answer 1

i think this is how it goes.

tan2x + 4x = 2(1 + 2x)

tan2x + 4x = 2 + 4x (open the brackets by multiplying the numbers in the brackets with the number out of the bracket)

*now bring the unknowns(x) to one side ( minus both sides with 4x to eliminate the unknown in the right)

    tan2x + 4x - 4x = 2

    tan2x = 2

(let only the unknown be in the left. when the tan is brought to the right, it&#039;ll be come tan^ -1)

   2x = tan^ -1(2)

   2x = 63.435

    x = 63.435/2

    x = 31.717 degrees

hope this answers ur quest..^_^

Answer 2

We want:

0 &lt; x &lt; 360

0 &lt; 2x &lt; 720

That means that, when it comes to finding inverse tan, we have two full revolutions to find the inverse, and hence, the equation will have no less than four solutions.

tan(2x) + 4x  = 2(1 +2x)

tan(2x) + 4x = 2 + 4x

tan(2x) = 2

2x = tan^-1(2)

or tan^-1(2) + 180

or tan^-1(2) + 360

or tan^-1(2) + 540

x = tan^-1(2) / 2

or tan^-1(2) / 2 + 90

or tan^-1(2) / 2 + 180

or tan^-1(2) / 2 + 270

x = 31.72 or 121.72 or 211.72 or 301.72