What is the general solution for 2sec^2(x)=3tan(x)+1 ?

The general solution for 2sec^2(x)=3tan(x)+1 is x= pi/4+pin,x=0.46364…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sec^2(x)=3tan(x)+1

2 sec^{2} (x) = 3 tan (x) + 1

x = \frac{π}{4} + πn, x = 0.46364 \dots + πn

Solution steps

2 sec^{2} (x) = 3 tan (x) + 1

Subtract

3 tan (x) + 1

from both sides

2 sec^{2} (x) - 3 tan (x) - 1 = 0

Rewrite using trig identities

1 + 2 tan^{2} (x) - 3 tan (x) = 0

Solve by substitution

tan (x) = 1, tan (x) = \frac{1}{2}

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = \frac{1}{2} : x = arctan (\frac{1}{2}) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = 0.46364 \dots + πn

2 sec (t) = tan^{2} (t) + 1

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

8 cos (2 x) = 43

cos^{2} (θ) - sin^{2} (θ) = 1

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

What is the general solution for 2sec^2(x)=3tan(x)+1 ?
The general solution for 2sec^2(x)=3tan(x)+1 is x= pi/4+pin,x=0.46364…+pin