What is the general solution for 1-tan(-x)=sec(-x) ?

The general solution for 1-tan(-x)=sec(-x) is x=2pin

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

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

x = 2 πn

Solution steps

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

Rewrite using trig identities

1 + tan (x) = sec (x)

Subtract

sec (x)

from both sides

1 + tan (x) - sec (x) = 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{π}{4} + 2 πn, x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

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

Solve

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

x = 2 πn, x = 2 πn + \frac{π}{2}

Since the equation is undefined for:

2 πn + \frac{π}{2}

x = 2 πn

cos (2 x - a) = sin (3 x)

x, 2 cos (x) = 3

41 sin^{2} (x) + 32 sin (x) - 9 = 0

cos (x - 3 0^{\circ}) = 2 sin (x)

sin (θ) - 3 cos (θ) = 2

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