What is the general solution for 2csc(x)cot(x)= 4/3 ?

The general solution for 2csc(x)cot(x)= 4/3 is x= pi/3+2pin,x=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2csc(x)cot(x)= 4/3

2 csc (x) cot (x) = \frac{4}{3}

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

Solution steps

2 csc (x) cot (x) = \frac{4}{3}

Subtract

\frac{4}{3}

from both sides

2 csc (x) cot (x) - \frac{4}{3} = 0

Simplify

2 csc (x) cot (x) - \frac{4}{3} : \frac{6 csc ( x ) cot ( x ) - 4}{3}

\frac{6 csc ( x ) cot ( x ) - 4}{3} = 0

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

6 csc (x) cot (x) - 4 = 0

Express with sin, cos

\frac{- 4 sin ^{2} ( x ) + 6 cos ( x )}{sin ^{2} ( x )} = 0

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

- 4 sin^{2} (x) + 6 cos (x) = 0

Rewrite using trig identities

- (1 - cos^{2} (x)) \cdot 4 + 6 cos (x) = 0

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 2 :

No Solution

Combine all the solutions

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

cos (t) = \frac{24}{25}

sec^{2} (t) + 2 sec (t) = 0

sin (27 0^{\circ} + x) - cos (18 0^{\circ} - x) = - sin (x)

9 cos (3 x) = 0

16 (l) cos (θ) = 5 sin (2 θ) (2 l)

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