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

The general solution for sin(x)tan(x)-(sqrt(2))/2 tan(x)=0 is x=pin,x= pi/4+2pin,x=(3pi)/4+2pin

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sin(x)tan(x)-(sqrt(2))/2 tan(x)=0

sin (x) tan (x) - \frac{2}{2} tan (x) = 0

x = πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Solution steps

sin (x) tan (x) - \frac{2}{2} tan (x) = 0

Factor

sin (x) tan (x) - \frac{2}{2} tan (x) : tan (x) (sin (x) - \frac{1}{2})

tan (x) (sin (x) - \frac{1}{2}) = 0

Solving each part separately

tan (x) = 0 or sin (x) - \frac{1}{2} = 0

tan (x) = 0 : x = πn

sin (x) - \frac{1}{2} = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (θ) = - 2, 0 \leq θ < 4 π

- sin^{2} (x) + cos^{2} (x) = sin (x) + 1

2 cos (x) + 2 = 4 sin^{2} (x)

tan (x) + cot (x) = 5

5 sin^{2} (θ) + 12 sin (θ) + 7 = 0

What is the general solution for sin(x)tan(x)-(sqrt(2))/2 tan(x)=0 ?
The general solution for sin(x)tan(x)-(sqrt(2))/2 tan(x)=0 is x=pin,x= pi/4+2pin,x=(3pi)/4+2pin