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If A = 5^(@) then the value of expressio...

If A = `5^(@)` then the value of expression ((`secA)/((1 - 4sin^(2)A)) + (cosec A)/((4 cos^(2)A -1)))^(2)` is :

Text Solution

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(24) Let E = `((secA)/((1-4sin^(2)A))+ (cosecA)/(4cos^(2)A -1))^(2) = ((1)/(cosA(1 - 4 + 4cos^(2)A)) + (1)/(sinA (3 - 4sin^(2)A)))`
`= ((1)/(4 cos^(3)A - 3cosA) + (1)/(3 sinA - 4 sin^(3)A)) = (sec 3A + cosec3A)^(2)`
`= [(sqrt(6) - sqrt(2)) + (sqrt(6) + sqrt(2)]^(2)`
Hence , `(2sqrt(6))^(2) = 24.`
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