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

Options

A. 2
B. -2
C. `(1)/(2)`
D. `(-1)/(2)`

Answer

C

Explanation

`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).`