What is the general solution for 7tan(θ)sin(θ)-6tan(θ)=0 ?

The general solution for 7tan(θ)sin(θ)-6tan(θ)=0 is θ=pin,θ=1.02969…+2pin,θ=pi-1.02969…+2pin

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7tan(θ)sin(θ)-6tan(θ)=0

7 tan (θ) sin (θ) - 6 tan (θ) = 0

θ = πn, θ = 1.02969 \dots + 2 πn, θ = π - 1.02969 \dots + 2 πn

Solution steps

7 tan (θ) sin (θ) - 6 tan (θ) = 0

Factor

7 tan (θ) sin (θ) - 6 tan (θ) : tan (θ) (7 sin (θ) - 6)

tan (θ) (7 sin (θ) - 6) = 0

Solving each part separately

tan (θ) = 0 or 7 sin (θ) - 6 = 0

tan (θ) = 0 : θ = πn

7 sin (θ) - 6 = 0 : θ = arcsin (\frac{6}{7}) + 2 πn, θ = π - arcsin (\frac{6}{7}) + 2 πn

Combine all the solutions

θ = πn, θ = arcsin (\frac{6}{7}) + 2 πn, θ = π - arcsin (\frac{6}{7}) + 2 πn

Show solutions in decimal form

θ = πn, θ = 1.02969 \dots + 2 πn, θ = π - 1.02969 \dots + 2 πn

2 sin^{2} (x) - 7 cos (x) + 2 = 0

5 cos (θ) = 0

sin (2 θ) = 4 cos (θ)

tan (θ) = \frac{4}{4}

tan (θ) = \frac{4}{6}

What is the general solution for 7tan(θ)sin(θ)-6tan(θ)=0 ?
The general solution for 7tan(θ)sin(θ)-6tan(θ)=0 is θ=pin,θ=1.02969…+2pin,θ=pi-1.02969…+2pin