Question
Download Solution PDF3 sin2 x - 7 sin x + 2 = 0 का व्यापक हल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
3 sin2 x - 7 sin x + 2 = 0
अवधारणा:
sin x के व्यापक मान की अवधारणा का प्रयोग कीजिए।
\(x=\rm n\pi+(-1)^n \theta\)
गणना:
3 sin2 x - 7 sin x + 2 = 0
sin x = y प्रतिस्थापित कीजिए,
⇒3y2 - 7y + 2 = 0
⇒3y2 - 6y - y + 2 = 0
⇒3y(y - 2) - (y - 2) = 0
⇒(y - 2)(3y - 1) = 0
⇒y = 2 , 1/3
हम जानते हैं कि sin x की परास [-1,1] है, तो 2 इससे अधिक की सीमा में नहीं है,
⇒ sin x = 1/3
⇒ x = sin-1(1/3)
इसलिए व्यापक मान
\(\rm x={n\pi}+(-1)^n\sin^{-1}\frac{1}{3}\)
अतः विकल्प (3) सही है।
Last updated on May 26, 2025
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