What is the general solution for 4tan(x)+2sin(x)cos(x)=0 ?

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

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4tan(x)+2sin(x)cos(x)=0

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Express with sin, cos

\frac{4 sin ( x ) + 2 cos ^{2} ( x ) sin ( x )}{cos ( x )} = 0

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

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos^{2} (x) + 2 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

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

3 sin (x) + 6 cos (x) = 4

3 tan (2 x + 1) = 2

\frac{1}{( 1 + tan ( a ) )} = cot (a)

tan (2 x) - 2 = 3 tan (x)

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