Question:
If \(x = 5\cos B + 12\sin B\) and \(y = 5\sin B – 12\cos B\), then find the value of \(x^2 + y^2\).
यदि \(x = 5\cos B + 12\sin B\) और \(y = 5\sin B – 12\cos B\) है, तो \(x^2 + y^2\) का मान ज्ञात कीजिए।
Options:
- 169
- 144
- 225
- 196
- 169
- 144
- 225
- 196
Correct Answer: a)
Explanation:
\(x^2 + y^2 = (5\cos B + 12\sin B)^2 + (5\sin B – 12\cos B)^2\)
\(= 25(\cos^2 B + \sin^2 B) + 144(\sin^2 B + \cos^2 B) + 0\)
\(= 25(1) + 144(1) = 169\).
\(x^2 + y^2 = (5\cos B + 12\sin B)^2 + (5\sin B – 12\cos B)^2 = 25 + 144 = 169\)।