Choose the correct answer in each of the following questions:
`(cos38^(@)"cosec"52^(@))/(tan18^(@)tan35^(@)tan60^(@)tan72^(@)tan55^(@))=?`

Options

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

Answer

C

Explanation

`(cos38^(@)"cosec"52^(@))/(tan18^(@)tan35^(@)tan60^(@)tan72^(@)tan55^(@))=(cos38^(@)"cosec"(90^(@)-38^(@)))/((tan18^(@)tan72^(@))(tan35^(@)tan55^(@))tan60^(@))`
`(cos38^(@)sec38^(@))/(tan18^(@)tan(90^(@)-18^(@))tan35^(@)tan(90^(@)-35^(@))sqrt(3)) " " [because tan60^(@)=sqrt(3)]`
`=(1)/((tan18^(@)cot18^(@))(tan35^(@)cot35^(@))sqrt(3))=(1)/(sqrt(3)).`