What is the general solution for sec(x)+tan(x)=1,(0,2pi) ?

The general solution for sec(x)+tan(x)=1,(0,2pi) is No Solution for x\in\mathbb{R}

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sec(x)+tan(x)=1,(0,2pi)

sec (x) + tan (x) = 1, (0, 2 π)

No Solution for x \in R

Solution steps

sec (x) + tan (x) = 1, (0, 2 π)

Subtract

1

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

Solutions for the range

(0, 2 π)

x = \frac{3 π}{2}

Since the equation is undefined for:

\frac{3 π}{2}

No Solution for x \in R

cos^{2} (θ) - cos (θ) - 20 = 0

100.0191 = 180 - arctan (\frac{3.9254}{0.6936 - x})

- 9 sin (x) = 0

4 csc (θ) - 1 = - cot (θ) + 3 csc (θ)

cos (2 x) = \frac{7}{9}

What is the general solution for sec(x)+tan(x)=1,(0,2pi) ?
The general solution for sec(x)+tan(x)=1,(0,2pi) is No Solution for x\in\mathbb{R}