Trig
posted by Mark .
Solve the equation in the given domain
cos 4x + cos 2x = 0, 0<(or equal to) x < pi

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. 
Thanks. Makes sense. My problem was I was trying to use another double argument property.
Respond to this Question
Similar Questions

Trigonometry
There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these … 
Math  Solving for Trig Equations
Solve the following equation for 0 less than and/or equal to "x" less than and/or equal to 360  cos^2x  1 = sin^2x  Attempt: cos^2x  1  sin^2x = 0 cos^2x  1  (1  cos^2x) = 0 cos^2x  1  1 + cos^2x = 0 2cos^2x  2 = 0 (2cos^2x/2)= … 
Math  Solving Trig Equations
Solve each equation for o is less than and/or equal to theta is less than and/or equal to 360  sin^2x = 1 = cos^2x  Work: cos^2x  cos^2x = 0 0 = 0  Textbook Answers: 90 and 270  Btw, how would you isolate for cos^2x = 0? 
Math  Solving Trig Equations
What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x)  1 cos(x) (+/)\sqrt{1  cos^2(x)} = 2cos^2(x)  1 cos^2(x)(1  cos^2(x)) 
trig
2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= cos(x) 2sin(x) = … 
TRIG!
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1  (3/4)sin^2 2x work on one side only! Responses Trig please help!  Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 … 
Math/trig
Solve the equation in the given Domain: 1cos theta/ sin theta = sqr3, 0degrees <or equal to theta < 369 degrees cos4x + cos 2x =0, 0<or equal to x < pi 
Precalculus
Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π) Ive got the equation down to cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0 If you could tell me where to go from either of these … 
calculus
find max, min and saddle points of the give function f(x,y)=sin(x)+sin(y)+sin(x+y) 0<=x<=pi/4 0<=y<=pi/4 i have that dz/dx=cos(x)+cos(x+y) dz/dy=cos(y)+cos(x+y) and i set them equal to zero but im kinda confused on how … 
Trig
Solve each equation for the given domain. cos^2 theta + cos theta  1 = 0 for 0180.