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Cos 45 by sec 30 + cosec 30

Answer» Given, cos 45/(sec 30 + cosec 30)= (1/√2)/(2/√3 + 2) {since cos 45 = 1/√2, sec 30 = 2/√3, cosec 30 = 2}= (1/√2)/{(2 + 2√3)/√3}= (√3/√2)/(2 + 2√3)= √3/{√2*(2 + 2√3)}= √3/(2√2 + 2√3*√2)= √3/(2√2 + 2√6)So, cos 45/(sec 30 + cosec 30) = √3/(2√2 + 2√6)


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