Question

How do you find all solutions of the equations `cosx+sinxtanx=2` in the interval `[0,2pi)`?

Answer 1

`x=pi/3` or `x=5/3*pi`

Explanation:

We can write
`cos(x)+sin^2(x)/cos(x)=2`
`cos(x)+(1-cos^2(x))/cos(x)=2`
Multiplying by `cos(x)`
`cos^2(x)+1-cos^2(x)=2cos(x)`
this gives
`cos(x)=1/2`
`x=pi73`
or
`x=5/3*pi`