Question:
If \(\sin \theta + \text{cosec } \theta = 2\), what is \(\sin^{10} \theta + \text{cosec}^{10} \theta\)?
यदि \(\sin \theta + \text{cosec } \theta = 2\) है, तो \(\sin^{10} \theta + \text{cosec}^{10} \theta\) का मान क्या होगा?
Options:
- 2
- 1
- 0
- 10
- 2
- 1
- 0
- 10
Correct Answer: a)
Explanation:
\(\sin \theta + 1/\sin \theta = 2 \implies (\sin \theta – 1)^2 = 0 \implies \sin \theta = 1\).
\(1^{10} + 1^{10} = 1 + 1 = 2\).
\(1^{10} + 1^{10} = 1 + 1 = 2\).
\(\sin \theta = 1\) होने पर \(1^{10} + 1^{10} = 2\)।