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2cosA + secA = 2√2
Or, 2cosA + (1/cosA) = 2√2
Or, 2cos 2 A + 1 = 2√2 × cosA
Or, 2cos 2 A – 2√2 × cosA + 1 = 0
Or, 2cos 2 A - √2cosA - √2cosA + 1 = 0
Or, √2 × cosA × (√2cosA – 1) – 1 × (√2cosA – 1) = 0
Or, (√2 × cosA – 1) 2 = 0
Or, √2 × cosA – 1 = 0
So, cosA = (1/√2) = cos45 o
So, A = 45 o
2(sec 4 A + cosec 4 A) = 2 × (sec 4 45 o + cosec 4 45 o )
= 2 × [(√2) 4 + (√2) 4 ] = 2 × (4 + 4) = 2 × 8 = 16
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