What is the general solution for cos(x)cos(3x)-sin(x)sin(3x)=0 ?

The general solution for cos(x)cos(3x)-sin(x)sin(3x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

cos (x + 3 x) = 0

General solutions for

cos (x + 3 x) = 0

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

Solve

x + 3 x = \frac{π}{2} + 2 πn : x = \frac{π}{8} + \frac{πn}{2}

Solve

x + 3 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

(cot (θ) - 1) (sin (θ) - 1) = 0

cos (2 x) = 2 sin^{2} (x)

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

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

3 cos (3 x) = 0

What is the general solution for cos(x)cos(3x)-sin(x)sin(3x)=0 ?
The general solution for cos(x)cos(3x)-sin(x)sin(3x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2