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

The general solution for cos(5x)cos(x)+sin(5x)sin(x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2

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

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

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

Solution steps

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

Rewrite using trig identities

cos (5 x - x) = 0

General solutions for

cos (5 x - x) = 0

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

Solve

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

Solve

5 x - 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}

sin (θ) = \frac{5 n + 1}{3} - 2 n

cosh (x) - 1 = 0

arctan (θ) = arctan (\frac{92}{44})

10 cos (x) - 52 = 0

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

What is the general solution for cos(5x)cos(x)+sin(5x)sin(x)=0 ?
The general solution for cos(5x)cos(x)+sin(5x)sin(x)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2