V13 Suppose that csc and Solutionthetaxsay given cscx sqrt

Solution

theta=x(say.....

given cscx = sqrt13/3 ,pi/2 x<pi ( II quadrant

sinx = 1/cscx = 3/sqrt13

cosx = - 2/sqt13

sin(x/2) = sqrt[ (1-cosx)/2] = sqrt[ (1-2/sqrt13)/2] = sqrt[ (sqrt13-2)/2*sqt13]

tan(x/2) = -sinx/(1+cosx) =- [3/sqrt13 ] /(1+2/sqrt13) = -3/(sqrt13+2)