Question:
Which of the following is true when x = SinA + CosA; y = SecA + CosecA?
निम्नलिखित में से कौन सा सत्य है जब x = SinA + CosA; y = SecA + CosecA है?
Options:
- a) y + 2x = x2 y
- b) y(1 + x2 ) = 2x
- c) y(1 – 2×2 ) = x
- d) y – 2x = x2 y
- a) y + 2x = x² y
- b) y(1 + x²) = 2x
- c) y(1 – 2x²) = x
- d) y – 2x = x² y
correct answer : a)
Explanation:
Given x = sin A + cos A and y = sec A + cosec A = 1/cos A + 1/sin A = (sin A + cos A) / (sin A * cos A) = x / (sin A * cos A) => sin A * cos A = x / y. We know x^2 = (sin A + cos A)^2 = sin^2 A + cos^2 A + 2 sin A cos A = 1 + 2(x/y) => x^2 = 1 + 2x/y. Multiplying by y: x^2 * y = y + 2x => y + 2x = x^2 * y.
दिया गया है x = sin A + cos A और y = sec A + cosec A = 1/cos A + 1/sin A = (sin A + cos A) / (sin A * cos A) = x / (sin A * cos A) => sin A * cos A = x / y। हम जानते हैं x² = (sin A + cos A)² = sin² A + cos² A + 2 sin A cos A = 1 + 2(x/y) => x² = 1 + 2x/y। y से गुणा करने पर: x² * y = y + 2x => y + 2x = x² * y।