Questions
The value of k if the equation 2 cos x + cos 2kx = 3 has only one solution is
a
0
b
2
c
2
d
12
detailed solution
Correct option is C
2cosx+cos2kx=3⇒ 21−2sin2x2+1−2sin2kx=3⇒ 2sin2x2+sin2kx=0---1Since sin2x2 and sin2kx are both non-negative, Eq.(1)is possible only if sin2x2=0 and sin2kx=0x=0,±2π,±4π,…But for Eq. (1) to have unique solution, the possible value of k is irrational.∴ k=2 is the possible option.Talk to our academic expert!
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