Question

Let x be an angle measure and let the real numbers a, b, c, cos x be such that they make the following equation true:a cos² x + b cos +c= 0Write the equivalent quadratic equation for a, b, c, cos 2x. Compare the given and the obtained equality for a = 4, b = 2,c=-1.​

Answer 1

Answer:

4cos²x/2 - 2cosx/2 -1 =0

Step-by-step explanation:

Given,

a=4, b=2 and c=-1

acos²x+bcosx+c=0

4cos²x+2cosx-1=0

cosx = [-2+√2²-4×4×-1]/2×4

cosx = (-1+√5)/4

x = 72°

Now,

a=4, b=2 ,c=-1 and

cos2x = cos144 = cos(180-36)

= -cos36 = -cosx/2

eqⁿ :

4cos²x/2 - 2cosx/2 -1 =0.