What is the general solution for (tan(x))/(cos(x))= 2/3 ?

The general solution for (tan(x))/(cos(x))= 2/3 is x= pi/6+2pin,x=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(tan(x))/(cos(x))= 2/3

\frac{tan ( x )}{cos ( x )} = \frac{2}{3}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

\frac{tan ( x )}{cos ( x )} = \frac{2}{3}

Subtract

\frac{2}{3}

from both sides

\frac{tan ( x )}{cos ( x )} - \frac{2}{3} = 0

Simplify

\frac{tan ( x )}{cos ( x )} - \frac{2}{3} : \frac{3 tan ( x ) - 2 cos ( x )}{3 cos ( x )}

\frac{3 tan ( x ) - 2 cos ( x )}{3 cos ( x )} = 0

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

3 tan (x) - 2 cos (x) = 0

Express with sin, cos

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

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

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

Rewrite using trig identities

- (1 - sin^{2} (x)) \cdot 2 + 3 sin (x) = 0

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

cos (x) = 1.22719

cos (a) = \frac{5}{5}

5 sec^{2} (x) - 5 = 0, 0 \leq x < 2 π

2 sin (5 x) + 3 = 2

What is the general solution for (tan(x))/(cos(x))= 2/3 ?
The general solution for (tan(x))/(cos(x))= 2/3 is x= pi/6+2pin,x=(5pi)/6+2pin