What will be the sum of the roots of the equation tan^233x=cos 2x-1 lying in the interval [pi,314]. please explain the steps also.

cos 2x=1-2(sin x)^2

 

therefor equation becomes

tan^2(33x)=-2(sin x)^2

 

clearly we can see LHS is always greater than or equal to zero and RHS is always less than or equal to zero therefor for both side to be equal both should be zero.

 

therfor slutions are pi,2*pi,3*pi...............................100*pi

 

sum of solutions =5050pi