The number of solutions of the equation , is
- A.3
- B.5
- C.7
- D.4
Show answer and solution
Correct option: B
Solution
The left side 1 + sin⁴x ≥ 1, and the right side cos²3x ≤ 1. So equality holds only when both sides equal 1, meaning cos²3x = 1 AND sin⁴x = 0 simultaneously.
sin⁴x = 0 → x = nπ (integer multiples of π).
cos²3x = 1 → 3x = mπ → x = mπ/3.
Both conditions hold when x = nπ satisfies x = mπ/3, which is always true (take m = 3n). So solutions are x = nπ.
In [-5π/2, 5π/2], the integer multiples of π are: -2π, -π, 0, π, 2π — that's 5 solutions.
The answer is 5.
sin⁴x = 0 → x = nπ (integer multiples of π).
cos²3x = 1 → 3x = mπ → x = mπ/3.
Both conditions hold when x = nπ satisfies x = mπ/3, which is always true (take m = 3n). So solutions are x = nπ.
In [-5π/2, 5π/2], the integer multiples of π are: -2π, -π, 0, π, 2π — that's 5 solutions.
The answer is 5.
[JEE Main 2019 · 12 April · Shift I]