2020 · Q52
Consider the following statements:
- 1The equation 2sin²θ − cosθ + 4 = 0 is possible for all θ.
- 2tanθ + cotθ cannot be less than 2, where 0 < θ < π/2.
Which of the above statements is/are correct?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
2sin^2(theta)-cos(theta)+4 = 0 gives cos(theta) = 1.5 or -2, both impossible, so statement 1 is false. tan(theta)+cot(theta) = 2/sin(2theta) >= 2 on (0, pi/2), so statement 2 is true. Statement 2 only - option (B).