What is the general solution for 2sin(θ)sec(θ)=4sin(θ) ?

The general solution for 2sin(θ)sec(θ)=4sin(θ) is θ=2pin,θ=pi+2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

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2sin(θ)sec(θ)=4sin(θ)

2 sin (θ) sec (θ) = 4 sin (θ)

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

Solution steps

2 sin (θ) sec (θ) = 4 sin (θ)

Subtract

4 sin (θ)

from both sides

2 sin (θ) sec (θ) - 4 sin (θ) = 0

Factor

2 sin (θ) sec (θ) - 4 sin (θ) : 2 sin (θ) (sec (θ) - 2)

2 sin (θ) (sec (θ) - 2) = 0

Solving each part separately

sin (θ) = 0 or sec (θ) - 2 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

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

Combine all the solutions

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

sec (x - \frac{π}{7}) cos (x - \frac{π}{7}) = sin (x - \frac{π}{7})

cos (x) = \frac{17}{28}

sec^{4} (x) - 4 sec^{2} (x) = 0

\frac{cos ( x )}{sec ( x )} - \frac{sin ( x )}{csc ( x )} = 1

tan (x) = \frac{12}{35}

What is the general solution for 2sin(θ)sec(θ)=4sin(θ) ?
The general solution for 2sin(θ)sec(θ)=4sin(θ) is θ=2pin,θ=pi+2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin