2018 · Q67
Consider the following statements :
- 1θ + θ can never be equal to 1.5.
- 2² θ + ² θ can never be less them 4.
Which of the statements given above is/are correct ?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- D. Neither 1 nor 2
Explanation
Statement 1: sin(theta) + cos(theta) = sqrt(2) sin(theta + 45 degrees) <= sqrt(2) approx 1.414 < 1.5, so it can never equal 1.5: true. Statement 2: sec^2(theta) + cosec^2(theta) = 1/(sin^2(theta) cos^2(theta)) = 4/sin^2(2 theta) >= 4: true. Both statements are correct. Hence option C.