What is the general solution for sec(x)+3tan(x)=1+2tan(x) ?

The general solution for sec(x)+3tan(x)=1+2tan(x) is x=2pin+2pi

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sec(x)+3tan(x)=1+2tan(x)

sec (x) + 3 tan (x) = 1 + 2 tan (x)

x = 2 πn + 2 π

Solution steps

sec (x) + 3 tan (x) = 1 + 2 tan (x)

Subtract

1 + 2 tan (x)

from both sides

sec (x) + tan (x) - 1 = 0

Express with sin, cos

\frac{1 - cos ( x ) + sin ( x )}{cos ( x )} = 0

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

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

Rewrite using trig identities

1 + 2 sin (x - \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x - \frac{π}{4}) = - 1

Divide both sides by

2

sin (x - \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (x - \frac{π}{4}) = - \frac{2}{2}

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn, x - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

Solve

x - \frac{π}{4} = \frac{7 π}{4} + 2 πn : x = 2 πn + 2 π

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

Since the equation is undefined for:

2 πn + \frac{3 π}{2}

x = 2 πn + 2 π

2 sin (3 x) = 0

x, cos (x) - sin (x + y) = 0

sin (x) = - cos (4 x)

cos (θ) = \frac{2}{3 38}

sec (x) cos (x) = sin (x)

What is the general solution for sec(x)+3tan(x)=1+2tan(x) ?
The general solution for sec(x)+3tan(x)=1+2tan(x) is x=2pin+2pi