What is the general solution for sec(x)-sec(x)tan(x)=0 ?

The general solution for sec(x)-sec(x)tan(x)=0 is x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

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

Factor

sec (x) - sec (x) tan (x) : - sec (x) (tan (x) - 1)

sec (x) - sec (x) tan (x)

Factor out common term

- sec (x)

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

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

Solving each part separately

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

sec (x) = 0 :

No Solution

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

Move

1

to the right side

tan (x) - 1 = 0

Add

1

to both sides

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

Simplify

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn

4 sin^{2} (x) = 3, 0 \leq x \leq 18 0^{\circ}

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

(3 cos (x) + 2 sin (x))^{2} + 5 sin^{2} (x) = 9 - 33

7 cos (2 x) = 7 sin^{2} (x) + 5

2 cos^{2} (x) - sin (x) = - 1

What is the general solution for sec(x)-sec(x)tan(x)=0 ?
The general solution for sec(x)-sec(x)tan(x)=0 is x= pi/4+pin