What is the general solution for sin(x)cos(x)=tan(x) ?

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

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sin(x)cos(x)=tan(x)

sin (x) cos (x) = tan (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (x) cos (x) = tan (x)

Subtract

tan (x)

from both sides

sin (x) cos (x) - tan (x) = 0

Express with sin, cos

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

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

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

Factor

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

sin (x) (cos (x) + 1) (cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or cos (x) + 1 = 0 or cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) + 1 = 0 : x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos (x) = \frac{2}{4}

sin (x) - sin (x) \cdot cos (x) = 0

1 - 1 tan^{2} (2 x) = sec^{2} (2 x)

10 tan (θ) - 4.9 (\frac{10}{13 cos ( θ )})^{2} = 0

1 - cos^{2} (θ) - 6959 cos (θ) = 0

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