Find the values of theta ,Θ that satisfy the equation. 2cot2Θ = 4 - cosecΘ, for values of 180 degrees < Θ < 360 degreesThanks,Vishnu

Deer Vishnu

2cot²Θ = 4 - cosecΘ

or 2 cosec²Θ +CosecΘ -6 =0

which gives

CosecΘ =-2 and 3/2

but for 180<Θ<360

cosecΘ is negative

so CosecΘ=-2

SinΘ =-1/2

Θ =210 and 330  degree

Regards

Badiuddin