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03.of coseco-sino =m andseco-coso =1, Prove that(min 53 min 3=1. |
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Answer» Given cosec theta - sin theta = m, sec theta - cos theta = nGiven that cosec theta - sin theta = m→ !/sin theta - sin theta = m⇒(1-sin² theta)/sin theta = m→ cos² theta/sin theta = mand sec theta - cos theta = n⇒1/costheta - cos theta =n→ (1-cos² theta)/cos theta = nsin² theta/cos theta = nNow (m²n)²/³ + (mn²)²/³⇒(cos⁴ theta/sin² theta × sin² theta/cos theta)²/³ + (cos² theta/sin theta× sin⁴ theta/cos² theta)²/³⇒ (cos³ theta)²/³ + (sin³ theta)²/³⇒cos² theta + sin² theta= 1 Hence proved |
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