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

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

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

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

x = 2 πn + π

Solution steps

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

Subtract

- tan (x) - 3

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 + π

Solve

x + \frac{π}{4} = \frac{7 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

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

Since the equation is undefined for:

2 πn + \frac{3 π}{2}

x = 2 πn + π

- 9.81 + 5 (32.17) (\frac{12}{2}) sin (θ) = 0

2 sin^{3} (x) - sin^{2} (x) - 2 sin (x) + 1 = 0

2 sin (x) = - 2

3 sin (x) = sin (x) + 1

sin (4 x) = sin (x)

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