What is the general solution for cos(4x)cos(x)-sin(4x)sin(x)= 1/2 ?

The general solution for cos(4x)cos(x)-sin(4x)sin(x)= 1/2 is x= pi/(15)+(2pin)/5 ,x= pi/3+(2pin)/5

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cos(4x)cos(x)-sin(4x)sin(x)= 1/2

cos (4 x) cos (x) - sin (4 x) sin (x) = \frac{1}{2}

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Solution steps

cos (4 x) cos (x) - sin (4 x) sin (x) = \frac{1}{2}

Rewrite using trig identities

cos (4 x + x) = \frac{1}{2}

General solutions for

cos (4 x + x) = \frac{1}{2}

4 x + x = \frac{π}{3} + 2 πn, 4 x + x = \frac{5 π}{3} + 2 πn

Solve

4 x + x = \frac{π}{3} + 2 πn : x = \frac{π}{15} + \frac{2 πn}{5}

Solve

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

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

tan (θ) = \frac{7}{3}

7 cos (B) - 13 = 0

cos (a) = \frac{1}{3}

tan (θ) = - \frac{7}{4}

2 sin (x) tan (x) + 1 = tan (x) + 2 sin (x)

What is the general solution for cos(4x)cos(x)-sin(4x)sin(x)= 1/2 ?
The general solution for cos(4x)cos(x)-sin(4x)sin(x)= 1/2 is x= pi/(15)+(2pin)/5 ,x= pi/3+(2pin)/5