Which of the following equations is/are possible?<br>I. \sin^{2}\theta=\frac{(x+y)^{2}}{4xy}, where x, y are positive unequal real quantities.<br>II. \sin \theta+\cos \theta=x+\frac{1}{x}, where x is a positive real quantity.<br>Select the correct answer using the code given below:
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
For I: (x+y)^2 \gt 4xy when x \neq y, making \sin^2\theta \gt 1 which is impossible. For II: x + \frac{1}{x} \geq 2, but the maximum value of \sin\theta + \cos\theta is \sqrt{2} \approx 1.414, which is also impossible.
Related questions on Trigonometry
- Two poles are situated 24 m apart and their heights differ by 10 m. What is the distance between their tips?
- If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of $(\tan^2 \...
- For 0 < \theta < \frac{\pi}{2}, consider the following : I. $(\tan^4 \theta + \tan^6 \theta)(\cot^4 \theta + \cot^6 \theta) = \sec^2 \the...
- If 3\sin \theta + 4\cos \theta = 5, then what is a value of 4\tan \theta + 3\cot \theta ?
- At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m toward...