What is the general solution for cos(3x)cos(9x)+sin(3x)sin(9x)=0 ?

The general solution for cos(3x)cos(9x)+sin(3x)sin(9x)=0 is x=-pi/(12)-(pin)/3 ,x=-pi/4-(pin)/3

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cos(3x)cos(9x)+sin(3x)sin(9x)=0

cos (3 x) cos (9 x) + sin (3 x) sin (9 x) = 0

x = - \frac{π}{12} - \frac{πn}{3}, x = - \frac{π}{4} - \frac{πn}{3}

Solution steps

cos (3 x) cos (9 x) + sin (3 x) sin (9 x) = 0

Rewrite using trig identities

cos (3 x - 9 x) = 0

General solutions for

cos (3 x - 9 x) = 0

3 x - 9 x = \frac{π}{2} + 2 πn, 3 x - 9 x = \frac{3 π}{2} + 2 πn

Solve

3 x - 9 x = \frac{π}{2} + 2 πn : x = - \frac{π}{12} - \frac{πn}{3}

Solve

3 x - 9 x = \frac{3 π}{2} + 2 πn : x = - \frac{π}{4} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}, x = - \frac{π}{4} - \frac{πn}{3}

cos (2 x) + 5 sin (x) + 2 = 0, 0 \leq x < 2 π

8 - 12 sin^{2} (θ) = 4 cos^{2} (θ)

\frac{sin ( 3 4 ^{\circ} )}{12} = \frac{sin ( x )}{15}

3 - 3 cos (θ) = \frac{3}{2} sec (θ)

18 sec^{2} (x) - 3 tan (x) = 21

What is the general solution for cos(3x)cos(9x)+sin(3x)sin(9x)=0 ?
The general solution for cos(3x)cos(9x)+sin(3x)sin(9x)=0 is x=-pi/(12)-(pin)/3 ,x=-pi/4-(pin)/3