2015 · Q71
Consider the following statements :
- 1There exists at least one value of x between 0 and \;π/2 which satisfies the equation ^{4}x - 2²x - 1 = 0
- 21.5 is greater than 1.5.
Which of the above statements is/are correct?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1: with u = sin²x, sin⁴x − 2sin²x − 1 = 0 becomes u² − 2u − 1 = 0, whose roots 1±√2 lie outside [0, 1] — no x in (0, π/2) satisfies it, so statement 1 is false. Statement 2: 1.5 rad ≈ 86° > 45°, so sin(1.5) > cos(1.5) — true. Hence '2 only' (option B).