What is the general solution for sin(5x)cos(x)-cos(5x)sin(x)=0 ?

The general solution for sin(5x)cos(x)-cos(5x)sin(x)=0 is x=(pin)/2 ,x= pi/4+(pin)/2

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sin(5x)cos(x)-cos(5x)sin(x)=0

sin (5 x) cos (x) - cos (5 x) sin (x) = 0

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

Solution steps

sin (5 x) cos (x) - cos (5 x) sin (x) = 0

Rewrite using trig identities

sin (5 x - x) = 0

General solutions for

sin (5 x - x) = 0

5 x - x = 0 + 2 πn, 5 x - x = π + 2 πn

Solve

5 x - x = 0 + 2 πn : x = \frac{πn}{2}

Solve

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

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

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

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

sin (x) = 6946

sin (2 x) - \frac{3}{2} = 0, - 2 π \leq x \leq 2 π

\frac{sec ( x ) + tan ( x )}{cot ( x ) + cos ( x )} = sec^{2} (x)

What is the general solution for sin(5x)cos(x)-cos(5x)sin(x)=0 ?
The general solution for sin(5x)cos(x)-cos(5x)sin(x)=0 is x=(pin)/2 ,x= pi/4+(pin)/2