Question

solve for all real numbers, 2cos^2x - 1 = cosx

Answer 1

Answer:

Hence solution is

{0,2π3,4π3}

Step-by-step explanation:

I mentally did that so don't blame me!

Answer 2

Answer:

Solution is

{

0

,

2

π

3

,

4

π

3

}

Explanation:

2

cos

2

x

−

cos

x

−

1

=

0

can be written as

2

cos

2

x

−

2

cos

x

+

cos

x

−

1

=

0

or 2cosx

(cosx−1)+1(cosx−1)=0

or

(2cosx+1)

(cosx−m1)=0

∴

either

2cosx+1=0

i.e.

cosx=−12 and in the interval [,2π) x=2π3 or 4π3

or

cosx−1= i.e. cosx=1 and in given interval x=0 .

Hence solution is

{0,2π3,4π3}