Expert Answers
ishpiro eNotes educator| Certified Educator

First, simplify the left side of the equation using the trigonometric identity for tangent:

`tanx = sinx/cosx`

cosx tanx will become

`cosx * sinx/cosx = sinx`

Then, the simplified equation we now have to solve is

`sinx = 1/2`

The values of angle x which sign equals 1/2 are 30 degrees and 150 degrees, or `pi/6` and `(5pi)/6` radians.

Since sine is a periodic function with the period of `2pi` , any angle obtained by adding an integer multiple of `2pi` to `pi/6` and `(5pi)/6` will have the same sine.

So, all solutions of this equation are

`x = pi/6 + 2pik`  and `x = (5pi)/6 + 2pik` ,

where k is an integer: `k = 0, +-1, +-2, ...`

tonys538 | Student

The equation cos x*tan x=1/2 has  to be solved for x.

First, use the relation `tan x = (sin x)/(cos x)` to simplify the equation

`cos x*tan x=1/2`

`cos x*((sin x)/(cos x))=1/2`

`sin x = 1/2`

`x = sin^-1(1/2)`

x = 30, x = 150 degrees

Now the sine function is periodic in nature and the value of sin x repeats after an interval of 360 degrees.

This gives the general solution of the equation as x = 30 + n*360 and x = 150 + n*360 degrees.