Solve the equations:
`cot theta + cosec theta = sqrt(3)`

Answer

`theta=2n pi+pi/3, n in Z`

Explanation

`cot theta + cosec theta = sqrt(3)`
or `(cos theta)/(sin theta)+1/(sin theta)=sqrt(3)`
or `cos theta +1 = sqrt(3) sin theta`
or `sqrt(3) sin theta - cos theta=1` ...(i)
or `2 cos (theta +pi/3)=-1`
or `cos (theta + pi/3)=-1/2`
or `cos (theta + pi/3)= "cos" (2 pi)/3`
`rArr theta +pi/3=2 n pi pm (2pi)/3, n in Z`
or `theta = 2n pi pm (2pi)/3 - pi/3, n in Z`
`:. theta =2npi +pi/3, n in Z`
or `theta =2 n pi - pi =(2n-1) pi, n in Z`
But `theta` cannot be equal to `(2n-1)pi` as it makes `sin theta=0`.
Hence, `theta=2n pi +pi/3, in Z`.