KVPY2018MathematicsTrigonometric Equations
The number of real solutions x of the equation cos 2 x sin 2 x + 1 1 + x 2 = cos 2 x + sec 2 x is
Options
- A0
- B1
- C2
- Dinfinite
Correct answer
B. 1
Step-by-step solution
We have, cos 2 x sin 2 x + 1 1 + x 2 = cos 2 x + sec 2 x LHS = cos 2 x sin 2 x + 1 1 + x 2 cos 2 x sin 2 x + 1 1 + x 2 ≤ 2 RHS = cos 2 x + sec 2 x ≥ 2 LHS = RHS ∴   cos 2 x + sec 2 x = 2 at x = 0 Hence, only one solution.