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

The general solution for 2sec^2(2x)=3tan(2x)+1 is x= pi/8+(pin)/2 ,x=(0.46364…)/2+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{0.46364 \dots}{2} + \frac{πn}{2}

Solution steps

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

Subtract

3 tan (2 x) + 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

tan (2 x) = 1 : x = \frac{π}{8} + \frac{πn}{2}

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

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{0.46364 \dots}{2} + \frac{πn}{2}

4 cot (x) + 5 = 9

2 = \frac{1}{2} [1 + arctan (\frac{1}{1 + C})]

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

t, x = sin^{2} (t)

2 sin^{2} (θ) - 3 sin (θ) - 2 = 0, 0 \leq θ < 2 π

What is the general solution for 2sec^2(2x)=3tan(2x)+1 ?
The general solution for 2sec^2(2x)=3tan(2x)+1 is x= pi/8+(pin)/2 ,x=(0.46364…)/2+(pin)/2