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दाहरण 22. सिद्ध कीजिए किcot u—' =J2+3+V4+/6" |
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Answer» Converting Cot(π/24) into degrees by multiplying the angle by 180/π we can get Cot(π/24)= cot 7.5 cotA= (1+cos2A)/sin2A We can write Cot (15/2)= (1+cos15°)/sin15°……………(1) Now cos15°= cos (45°-30°) =cos45.cos30+sin45.sin30 =1/√2.√3/2+1/√2.1/2 => cos 15°= (1/4) (√6 + √2) Similarly sin15° = (1/4) (√6 - √2) Putting these values in eq. (1) Cot (15/2)= [1 + (1/4) (√6 + √2)] / [(1/4) (√6 - √2)]= (4 + √6 + √2) / (√6 - √2) On rationalisationCot (15/2)= [(4 + √6 + √2) * (√6 + √2)] / [(√6 - √2) * (√6 + √2)]= (4√6 + 6 + 2√3 + 4√2 + 2√3 + 2) / 4= (4√2 + 4√3 + 8 + 4√6) / 4= √2 + √3 + √4 + √6. |
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