Question

how do u find period, all angles and name 8 angles for these????????
1)cosxcos2x+sinxsin2x=sqrt(2)/2
2)5cosxsinx+2cosx=0

Answer 1

You have to know your expansion formulas
to recognize that
cosx cos2x + sinx sin2x = cos(x-2x)
= cos(-x)
but cos(-x) = cos(x)
so,
cosx = √2/2
x = 45° or 315°
in radians: x = π/4 or 7π/4
since the original = cosx, and the period of cosx = 360°, the period of the original is 360°
so add/subtract 360° to any answer to yield more answers until you have 8 of them
e.g. 45+360 = 405 , another answer

5cosxsinx + 2cosx=0
cosx(5sinx + 2) = 0
cosx = 0 or sinx = -2/5

if cosx =0, then x = 90° or 270°
if cosx = -2/5, x = appr. 113.6° or 246.4°
period again is 360° , etc

(it asked for all angles, no such thing there would be an infinite number of angles as solutions)