3cot2 theta 4 csc theta 1Solution3cot2 theta 4 csc theta 1 c

3cot^2 theta -4 csc theta =1

[csc^2 theta -cot^2 theta=1 is an identity =>cot^2 theta=csc^2 theta -1]

3(csc^2 theta -1) -4 csc theta =1

3csc^2 theta -3 -4csc theta =1

3csc^2 theta -4csc theta -4=0

3csc^2 theta -6csc theta+2csc theta -4=0

3csctheta(csctheta -2)+2(csctheta -2)=0

(csctheta -2)(3csctheta +2)=0

range of csctheta is (-infinity,-1)U(1,csctheta)

so csctheta-2 =0

csctheta=2

sintheta =1/2

theta =2n+(/6) ,2n+(5/6) where n is an integer