What is the general solution for 2tan(x)sin(x)-7sin(x)=0 ?

The general solution for 2tan(x)sin(x)-7sin(x)=0 is x=2pin,x=pi+2pin,x=1.29249…+pin

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2tan(x)sin(x)-7sin(x)=0

2 tan (x) sin (x) - 7 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = 1.29249 \dots + πn

Solution steps

2 tan (x) sin (x) - 7 sin (x) = 0

Factor

2 tan (x) sin (x) - 7 sin (x) : sin (x) (2 tan (x) - 7)

sin (x) (2 tan (x) - 7) = 0

Solving each part separately

sin (x) = 0 or 2 tan (x) - 7 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 tan (x) - 7 = 0 : x = arctan (\frac{7}{2}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (\frac{7}{2}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.29249 \dots + πn

sin^{2} (x) + sin (x) = 2

- 3 sin^{2} (θ) + 3 = - 10 cos (θ) - 3

cos (2 x) + 2 sin (x) = 1

cot (3 x) = \frac{3}{3}

tanh (z) = 0

What is the general solution for 2tan(x)sin(x)-7sin(x)=0 ?
The general solution for 2tan(x)sin(x)-7sin(x)=0 is x=2pin,x=pi+2pin,x=1.29249…+pin