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, ...`
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.