Match List I with II and select the correct answer using the code given below the lists

Options

A. `{:(A,B,C),(4,1,2):}`
B. `{:(A,B,C),(4,2,1):}`
C. `{:(A,B,C),(3,2,1):}`
D. `{:(A,B,C),(2,1,4):}`

Answer

B

Explanation

(A) `tan15^(@)=tan(45^(@)-30^(@))`
`=(1-(1)/(sqrt(3)))/(1+(1)/(sqrt(3)))=(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1)=(3+1-2sqrt(3))/(2)=2-sqrt(3)`
B `tan75^(@)=tan(45^(@)+30^(@))=(tan45^(@)+tan30^(@))/(1-tan45^(@)tan30^(@))`
`=(1+(1)/(sqrt(3)))/(1-(1)/(sqrt(3)))=(sqrt(3)+1)/(sqrt(3)-1)xx(sqrt(3)+1)/(sqrt(3))` (by Rationalizing)
`=2+sqrt(3)`
( C) `tan(105^(@))=tan(60^(@)+45)`
`=(sqrt(3)+1)/(1-sqrt(3))xx(1+sqrt(3))/(1+sqrt(3))=((sqrt(3)+1)^(2))/(1-3)`
`=(4+2sqrt(3))/(-2)=-2-sqrt(3)`
Hence , option (b) is correct.