Choose the correct answer in each of the following questions:
If ` "cosec" theta = sqrt(10) " then " sec theta=?`

Options

A. `(3)/(sqrt(10))`
B. `(sqrt(10))/(3)`
C. `(1)/(sqrt(10))`
D. `(2)/(sqrt(10))`

Answer

B

Explanation

`"cosec"theta=(AC)/(BC)=(sqrt(10))/(1)=(sqrt(10)x)/(x)rArrAC=sqrt(10)x and BC=x.`
`therefore AB^(2)=AC^(2)-BC^(2)=(sqrt(10)x)^(2)-(x^(2))=10x^(2)-x^(2)=9x^(2)`
`rArr AB=sqrt(9x^(2))=3x.`
`therefore sec theta =(AC)/(AB)=(sqrt(10)x)/(3x)=(sqrt(10))/(3).`