The value of `(sin300^(@).tan330^(@).sec420^(@))/(tan135^(@).sin210^(@).sec315^(@))` is

Options

A. `-1`
B. 1
C. `sqrt(2)`
D. `sqrt(3)`

Answer

C

Explanation

Given expression
`=(sin(360^(@)-60^(@)).tan(360^(@)-30^(@)).sec(360^(@)+60^(@)))/(tan(180^(@)-45^(@)).sin(180^(@)+30^(@)).sec(360^(@)-45^(@)))`
`=((-sin 60^(@)).(-tan 30^(@)).sec 60^(@))/((-tan 45^(@)).(-sin 30^(@)).sec 45^(@))`
`=(sin 60^(@).tan30^(@).sec60^(@))/(tan 45^(@).sin 30^(@).sec 45^(@))`
`= ((.sqrt(3))/(2).(1)/(sqrt(3)).2)/(1.(1)/(2).sqrt(2))=sqrt(2)`