What is the general solution for 7sin(θ)-1=5sin(θ) ?

The general solution for 7sin(θ)-1=5sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

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7sin(θ)-1=5sin(θ)

7 sin (θ) - 1 = 5 sin (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

7 sin (θ) - 1 = 5 sin (θ)

Solve by substitution

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

csc (θ) = - \frac{7}{3}

sin (θ) = \frac{5}{8}

arctan (2 x) + arctan (x) = \frac{π}{4}

tan (a) = 1

cos (2 θ) = 2, cos^{2} (θ) - 1 = 2, (- \frac{3}{5})^{2} - 1 = - \frac{7}{25}

What is the general solution for 7sin(θ)-1=5sin(θ) ?
The general solution for 7sin(θ)-1=5sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin