cot2theta4csctheta5Solutioncot2theta4csctheta5 we know cot2x

cot^2theta+4csctheta=-5

we know cot^2x +1 = cosec^2x

So, csc^2(theta) -1 + 4csctheta = -5

csc^2(theta) + 4csctheta = -4

csc^2(theta) + 4csctheta + 4 =0

(csctheta+2)^2 =0

csctheta = -2

sintheta = -1/2

Interval : [0, 2pi ) : theta = pi+pi/6 , 2pi - pi/6

theta = 7pi/6 , 11pi/6