Posted by **Mark** on Monday, November 14, 2011 at 11:15am.

Solve the equation in the given domain

cos 4x + cos 2x = 0, 0<(or equal to) x < pi

- Trig -
**Reiny**, Monday, November 14, 2011 at 1:33pm
use the identity

cos 2A = 2 cos^2 A - 1 on cos4A

cos 4A = 2cos^2 2A - 1

so

2cos^2 2A - 1 + cos 2A = 0

(2cos 2A -1)(cos 2A + 1) = 0

cos 2A = 1/2 or cos 2A = -1

2A = 60° or 300° or 2A = 180°

A = 30° or 150° or A = 90°

I guess I should have kept x instead of A, no big deal.

x = 30°, 90° , 150°

or

x = π/6, π/2, 5π/6

check:

if x=30° --- cos 120° + cos 60° = -1/2 + 1/2 = 0

if x=90 --- cos 360 + cos 180 = 1 - 1 =0

if x = 150 -- cos 600 + cos 300 = -1/2 + 1/2 = 0

all is good.

- Trig -
**Mark**, Monday, November 14, 2011 at 2:32pm
Thanks. Makes sense. My problem was I was trying to use another double argument property.

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