gen solutions to complex trigs...

[bar0029]

hi there,
is anyone able to help find the general solution to this equation:

cos(x) + cos(3x) = 1/2
 

[Linkage1992]

Is this with the calculator or without?

[chopz]

u mean the one in the sample 2010 questions, pretty sure without calc

[sajib_mostofa]

Thats a crazy Q

[costa94]

Use triple angle formula for the cos3x because you need to have only x in the brackets. From there let cos(x) = u and u get 4u^3 etc etc = 1/2, then solve.

[JinXi]

cos (x) + cos(3x) = 0.5
cos (x) + cos(2x)cos(2) - sin(2x)sin(x) = 0.5
cos (x) + (1-2sin^2(x))(cos(x))-2sin^2(x)cos(x)=0.5
cos (x) + cos(x)-2sin^2(x)cos(x)-2sin^2(x)cos(x)=0.5
2cos(x) - 4sin^2(x)cos(x)=0.5
2cos(x) -2((1-cos(2x))cos(x)) =0.5
2cos(x) - 2cos(x) + 2cos^2(x)=0.5
cos^2(x) = 0.25
cos(2x) = +- 0.25
2x = pi/3, 2pi/3 + kpi
x = pi/6, 2pi/6 + kpi/2

k= Natural Numbers.

Doubt we nid this in methods  u.u