Question

If the equation 2 cos x + cos 2kx = 3 has only one solution then k is

• A. 1
• B. A rational number
• C. An irrational number
• D. Integers

Answer 1

The correct option is C

An irrational number

As max. cos $\theta$ = 1, 2 cos x + cos 2kx = 3 is possible only when cos x = 1

and cos 2kx = 1,

i.e., cos x = 1 and sin kx = 0.

x = 2n $\pi$ and kx = n $\pi$.

$\text{If a is rational number, then there are infinite or no common solutions but a is irrational, the equation has only one solution i.e., x = 0}$