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Choose the correct answer in each of the following questions: `cos^(2)30^(@)cos^(2)45^(@)+4sec^(2)60^(@)+(1)/(2)cos^(2)90^(@)-2tan^(2)60^(@)=?`

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Choose the correct answer in each of the following questions:
`cos^(2)30^(@)cos^(2)45^(@)+4sec^(2)60^(@)+(1)/(2)cos^(2)90^(@)-2tan^(2)60^(@)=?`
A. `(73)/(8)`
B. `(75)/(8)`
C. `(81)/(8)`
D. `(83)/(8)`
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Correct Answer - D
`cos^(2)30^(@)cos^(2)45^(@)+4sec^(2)60^(@)+(1)/(2)cos^(2)90^(@)-2tan^(2)60^(@)`
`=((sqrt(3))/(2))^(2)*((1)/(sqrt(2)))^(2)+(4xx2^(2))+((1)/(2)xx0^(2))-2xx(sqrt(3))^(2)`
`=((3)/(4)xx(1)/(2))+16+0-6=(3)/(8)+10=(83)/(8).`
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