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

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

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

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

x = πn

Solution steps

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

Factor

2 sin (x) tan (x) + 5 tan (x) : tan (x) (2 sin (x) + 5)

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

Solving each part separately

tan (x) = 0 or 2 sin (x) + 5 = 0

tan (x) = 0 : x = πn

2 sin (x) + 5 = 0 :

No Solution

Combine all the solutions

x = πn

tan (3 x) = 3, 0 \leq x \leq 2 π

sin (3 x) cos (x) = - cos (3 x) sin (x)

6 sin^{2} (x) + sin (x) - 1 = 0

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

sin^{2} (x) - 7 cos (x) + 7 = 0

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