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

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

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2sin(x)+2sin(x)tan(x)=0

2 sin (x) + 2 sin (x) tan (x) = 0

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

Solution steps

2 sin (x) + 2 sin (x) tan (x) = 0

Factor

2 sin (x) + 2 sin (x) tan (x) : 2 sin (x) (tan (x) + 1)

2 sin (x) (tan (x) + 1) = 0

Solving each part separately

sin (x) = 0 or tan (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) + 1 = 0 : x = \frac{3 π}{4} + πn

Combine all the solutions

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

y, x = x (1 + tan (y))

- 9 cos^{2} (θ) + sin (θ) + 11 = - sin (θ) + 2

sin (θ) = 1 - 2 cos (θ)

6 sec^{2} (x) - 6 sec (x) = 12

sin (a) = \frac{2}{2}

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