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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

Verified by Experts

The correct Answer is:
24
Let` E = ((sec A)/( (1 - 4 sin^(2)A)) + ("cosec"A)/((4cos^(2)A -1)))^(2) = ((1)/(cos A ( 1-4 + 4 cos^(2)A)) + (1)/(sinA (3 -4 sin^(2)A)))`
` =((1)/(4cos^(3) A - 3cosA ) + (1)/(3 sin A - 4sin^(3)A)) = (sec 3A + "cosec"3A)^(2)`
` [(sqrt(6) - sqrt(2)) + (sqrt(6) + sqrt(2))]^(2) , " Hence " (2sqrt(6))^(2) = 24`.
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