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

The general solution for sec(x)=2cos(x) is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(x)=2cos(x)

sec (x) = 2 cos (x)

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solution steps

sec (x) = 2 cos (x)

Subtract

2 cos (x)

from both sides

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

Rewrite using trig identities

- \frac{2}{sec ( x )} + sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = - 2

sec (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sec (x) = - 2 : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

sec (5 \frac{θ}{4}) = 2, 0 < θ < 2 π

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

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

cos (2 x + \frac{π}{3}) = sin (3 x)

y, x = arcsin (y)

What is the general solution for sec(x)=2cos(x) ?
The general solution for sec(x)=2cos(x) is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin