What is the general solution for sin(θ)sec(θ)-sin(θ)=0 ?

The general solution for sin(θ)sec(θ)-sin(θ)=0 is θ=2pin,θ=pi+2pin

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sin(θ)sec(θ)-sin(θ)=0

sin (θ) sec (θ) - sin (θ) = 0

θ = 2 πn, θ = π + 2 πn

Solution steps

sin (θ) sec (θ) - sin (θ) = 0

Factor

sin (θ) sec (θ) - sin (θ) : sin (θ) (sec (θ) - 1)

sin (θ) (sec (θ) - 1) = 0

Solving each part separately

sin (θ) = 0 or sec (θ) - 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sec (θ) - 1 = 0 : θ = 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

r = 2 a cos (x)

tan (t) = - \frac{1}{3}, - π < t \leq π

sin (x) = \frac{- 4}{5}

16 = 7 - 7 cos (θ)

sin (θ) = \frac{5}{4}

What is the general solution for sin(θ)sec(θ)-sin(θ)=0 ?
The general solution for sin(θ)sec(θ)-sin(θ)=0 is θ=2pin,θ=pi+2pin