What is the general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 ?

The general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 is x= pi/(10)+(2pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(3x)cos(2x)+cos(3x)sin(2x)=1

sin (3 x) cos (2 x) + cos (3 x) sin (2 x) = 1

x = \frac{π}{10} + \frac{2 πn}{5}

Degrees

x = 1 8^{\circ} + 7 2^{\circ} n

Solution steps

sin (3 x) cos (2 x) + cos (3 x) sin (2 x) = 1

Rewrite using trig identities

sin (3 x) cos (2 x) + cos (3 x) sin (2 x)

Use the Angle Sum identity:

sin (s) cos (t) + cos (s) sin (t) = sin (s + t)

= sin (3 x + 2 x)

sin (3 x + 2 x) = 1

General solutions for

sin (3 x + 2 x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

3 x + 2 x = \frac{π}{2} + 2 πn

3 x + 2 x = \frac{π}{2} + 2 πn

Solve

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

3 x + 2 x = \frac{π}{2} + 2 πn

Add similar elements:

3 x + 2 x = 5 x

5 x = \frac{π}{2} + 2 πn

Divide both sides by

5

5 x = \frac{π}{2} + 2 πn

Divide both sides by

5

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

Simplify

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

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{π}{2}}{5} + \frac{2 πn}{5} : \frac{π}{10} + \frac{2 πn}{5}

\frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{2}}{5} = \frac{π}{10}

\frac{\frac{π}{2}}{5}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 5}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{π}{10}

= \frac{π}{10} + \frac{2 πn}{5}

x = \frac{π}{10} + \frac{2 πn}{5}

x = \frac{π}{10} + \frac{2 πn}{5}

x = \frac{π}{10} + \frac{2 πn}{5}

x = \frac{π}{10} + \frac{2 πn}{5}

tan^{2} (θ) + 4 tan (θ) = 3

3 cot (θ) + 7 = 0

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

sin^{2} (x) - cos (x) - 1 = 0

3 tan (2 θ) + 1 = 0

What is the general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 ?
The general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 is x= pi/(10)+(2pin)/5