What is the general solution for sec(θ)csc(θ)=2csc(θ) ?

The general solution for sec(θ)csc(θ)=2csc(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin

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sec(θ)csc(θ)=2csc(θ)

sec (θ) csc (θ) = 2 csc (θ)

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

sec (θ) csc (θ) = 2 csc (θ)

Subtract

2 csc (θ)

from both sides

sec (θ) csc (θ) - 2 csc (θ) = 0

Factor

sec (θ) csc (θ) - 2 csc (θ) : csc (θ) (sec (θ) - 2)

csc (θ) (sec (θ) - 2) = 0

Solving each part separately

csc (θ) = 0 or sec (θ) - 2 = 0

csc (θ) = 0 :

No Solution

sec (θ) - 2 = 0 : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

sin (A) = \frac{( 60 ) sin ( 15 5 ^{\circ} )}{97.73}

cos (θ) = 1 - cos (θ)

tan (θ) = - 1.5

tan (θ) = \frac{30}{20}

10 cos (θ) - 53 = 0

What is the general solution for sec(θ)csc(θ)=2csc(θ) ?
The general solution for sec(θ)csc(θ)=2csc(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin