What is the general solution for -4sec^2(x)+19=-4tan(x) ?

The general solution for -4sec^2(x)+19=-4tan(x) is x=-0.98279…+pin,x=1.19028…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-4sec^2(x)+19=-4tan(x)

- 4 sec^{2} (x) + 19 = - 4 tan (x)

x = - 0.98279 \dots + πn, x = 1.19028 \dots + πn

Solution steps

- 4 sec^{2} (x) + 19 = - 4 tan (x)

Subtract

- 4 tan (x)

from both sides

- 4 sec^{2} (x) + 19 + 4 tan (x) = 0

Rewrite using trig identities

15 + 4 tan (x) - 4 tan^{2} (x) = 0

Solve by substitution

tan (x) = - \frac{3}{2}, tan (x) = \frac{5}{2}

tan (x) = - \frac{3}{2} : x = arctan (- \frac{3}{2}) + πn

tan (x) = \frac{5}{2} : x = arctan (\frac{5}{2}) + πn

Combine all the solutions

x = arctan (- \frac{3}{2}) + πn, x = arctan (\frac{5}{2}) + πn

Show solutions in decimal form

x = - 0.98279 \dots + πn, x = 1.19028 \dots + πn

4 sin (x) + 6 = 6

tan (2 x - \frac{π}{6}) = \frac{- 1}{3}

2 cos (x) + 2 sin (x) = 1

sin (θ) = \frac{2}{13}, cos (θ) = \frac{3}{13}

cos (x) + 7 = 7

What is the general solution for -4sec^2(x)+19=-4tan(x) ?
The general solution for -4sec^2(x)+19=-4tan(x) is x=-0.98279…+pin,x=1.19028…+pin