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Choose the correct answer in each of the following questions: If `tan^(2)45^(@)-cos^(2)30^(@)=x sin45^(@) cos 45^(@) " then " x =?`

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Choose the correct answer in each of the following questions: If `tan^(2)45^(@)-cos^(2)30^(@)=x sin45^(@) cos 45^(@) " then " x =?`
A. 2
B. -2
C. `(1)/(2)`
D. `(-1)/(2)`
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1 Answer

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Correct Answer - C
`x=(tan^(2)45^(@)-cos^(2)30^(@))/(sin45^(@)cos45^(@))=(1-((sqrt(3))/(2))^(2))/(((1)/(sqrt(2))xx(1)/(sqrt(2))))=(1-(3)/(4))/((1)/(2))=(1)/(4)xx(2)/(1)=(1)/(2).`
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