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

The general solution for cos(x)+cos(3x)=0 is x= pi/4+pin,x=(3pi)/4+pin,x= pi/2+2pin,x=(3pi)/2+2pin

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

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

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

Solution steps

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

Rewrite using trig identities

2 cos (2 x) cos (x) = 0

Solving each part separately

cos (2 x) = 0 or cos (x) = 0

cos (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

cos (x) = 3

4 sin (2 x) = 0

4 cos^{2} (x) + 4 cos (x) = 1

sin (x) = \frac{1}{6}

tan (θ) = \frac{2}{5}

What is the general solution for cos(x)+cos(3x)=0 ?
The general solution for cos(x)+cos(3x)=0 is x= pi/4+pin,x=(3pi)/4+pin,x= pi/2+2pin,x=(3pi)/2+2pin