Number of solutions of the equation lying in the interval is
- A.0
- B.1
- C.2
- D.3
Show answer and solution
Correct option: C
Solution
The equation tan x + sec x = 2cos x becomes (sin x + 1)/cos x = 2cos x, so sin x + 1 = 2cos²x = 2(1 - sin²x). This gives 2sin²x + sin x - 1 = 0, factoring as (2sin x - 1)(sin x + 1) = 0. So sin x = 1/2 or sin x = -1. Sin x = 1/2 gives x = π/6 and x = 5π/6, both valid (cos x ≠ 0 at these points). Sin x = -1 gives x = 3π/2, but cos(3π/2) = 0 makes the original equation undefined. Thus exactly 2 valid solutions exist.
[1993]