Find the general solutions of each of the following equations :
1. `cosec x=-sqrt(2)`
(2) `tan3x=-1`.

Explanation

The general solution of `sin theta= sin alpha` is
`theta n pi +(-1)^(n)alpha, n in Z`
Now , `cosec x =- sqrt(2)`
`therefore sinx=-(1)/(sqrt(2))`
`therefore sinx=-sin.(pi)/(4)`
`therefore x=sin.(pi+(pi)/(4))......[because sin(pi+theta)=-sintheta]`
`therefore sinx=sin.(5pi)/(4)`
`therefore` The required general solution is
`x= n pi +(-1)^(n)((5pi)/(4)), n in Z`.
(2). The general solution of `tan theta =tan alpha is theta = n pi +alpha,n in Z`.
Now , `tan3x=-1=-tan.(pi)/(4).....[because tan.(pi)/(4)=1]`
`therefore 3x=tan(pi-(pi)/(4))`
`therefore tan3x=tan.(3pi)/(4)`
`therefore 3x= n pi +(3pi)/(4), n in Z " " therefore x =(n pi)/(4), n in Z`
`therefore` the requried general solution is `x=(n pi)/(3)+(pi)/(4), n in Z`.