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

The general solution for tan(2x)=cot(3x) is x= pi/(10)+(2pin)/5 ,x=(3pi}{10}+\frac{2pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(2x)=cot(3x)

tan (2 x) = cot (3 x)

x = \frac{π}{10} + \frac{2 πn}{5}, x = \frac{3 π}{10} + \frac{2 πn}{5}

Solution steps

tan (2 x) = cot (3 x)

Subtract

cot (3 x)

from both sides

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

Express with sin, cos

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

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

- cos (2 x) cos (3 x) + sin (2 x) sin (3 x) = 0

Rewrite using trig identities

- cos (2 x + 3 x) = 0

Divide both sides by

- 1

cos (2 x + 3 x) = 0

General solutions for

cos (2 x + 3 x) = 0

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

Solve

2 x + 3 x = \frac{π}{2} + 2 πn : x = \frac{π}{10} + \frac{2 πn}{5}

Solve

2 x + 3 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{10} + \frac{2 πn}{5}

x = \frac{π}{10} + \frac{2 πn}{5}, x = \frac{3 π}{10} + \frac{2 πn}{5}

sin (x) = \infty

- e^{- s i n (x)} (sin (x) + cos^{2} (x)) = 0

cos^{2} (β) - cot^{2} (β) = cos^{2} (β) cot^{2} (β)

4 tan (x) + 4 = 0, 0 \leq x < 2 π

cos^{3} (x) = cos (x), 0 \leq x < 2 π

What is the general solution for tan(2x)=cot(3x) ?
The general solution for tan(2x)=cot(3x) is x= pi/(10)+(2pin)/5 ,x=(3pi}{10}+\frac{2pin)/5