The number of solutions of the equation 1+sin4x=cos23x, x∈[-5π/2, 5π/2] is?

Correct option is A. 5
Given 1+sin4x=cos23x
As sin4x ∈ [0,1] ⇒ 1+sin4x ∈ [1,2]
And cos23x ∈ [0,1]
So the only common solution is 1+sin4x=1 and cos23x=1
⇒ sin4x=0 and sin23x=0
⇒ x=nπ and 3x=mπ ⇒ x=nπ and mπ/3
So the common solution will be x=kπ where k is an integer
For x ∈ [-5π/2, 5π/2], x = -2π, -π, 0, π, 2π
Number of solutions are 5