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

The general solution for 2cos(x)+tan(x)=sec(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(x)+tan(x)=sec(x)

2 cos (x) + tan (x) = sec (x)

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

2 cos (x) + tan (x) = sec (x)

Subtract

sec (x)

from both sides

2 cos (x) + tan (x) - sec (x) = 0

Express with sin, cos

\frac{- 1 + sin ( x ) + 2 cos ^{2} ( x )}{cos ( x )} = 0

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

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{1}{2}, sin (x) = 1

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin^{2} (x) = \frac{1}{2}

cos^{3} (\frac{π}{2})

arctan (\frac{1}{3})

sin (\frac{π}{2})

sin (\frac{5 π}{3})

What is the general solution for 2cos(x)+tan(x)=sec(x) ?
The general solution for 2cos(x)+tan(x)=sec(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin