What is the general solution for 2sin(2x)-5tan(2x)=0 ?

The general solution for 2sin(2x)-5tan(2x)=0 is x=pin,x= pi/2+pin

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2sin(2x)-5tan(2x)=0

2 sin (2 x) - 5 tan (2 x) = 0

x = πn, x = \frac{π}{2} + πn

Solution steps

2 sin (2 x) - 5 tan (2 x) = 0

Express with sin, cos

\frac{- 5 sin ( 2 x ) + 2 cos ( 2 x ) sin ( 2 x )}{cos ( 2 x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- 5 sin (2 x) + 2 cos (2 x) sin (2 x) = 0

Factor

- 5 sin (2 x) + 2 cos (2 x) sin (2 x) : sin (2 x) (2 cos (2 x) - 5)

sin (2 x) (2 cos (2 x) - 5) = 0

Solving each part separately

sin (2 x) = 0 or 2 cos (2 x) - 5 = 0

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

2 cos (2 x) - 5 = 0 :

No Solution

Combine all the solutions

x = πn, x = \frac{π}{2} + πn

75 = \frac{120}{4} \cdot cos (\frac{2 \cdot π \cdot x}{360}) + \frac{120}{2}

cot^{2} (x) + 2 = 2 csc (x)

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

15 cos^{2} (x) - 4 cos (x) - 3 = 0

- 3 sin^{2} (θ) + 3 = - cos (θ) + 2

What is the general solution for 2sin(2x)-5tan(2x)=0 ?
The general solution for 2sin(2x)-5tan(2x)=0 is x=pin,x= pi/2+pin