Choose the correct answer in each of the following questions:
`(2tan^(2)30^(@)sec^(2)52sin^(2)38^(@))/("cosec"^(2)70^(@)-tan^(2)20^(@))=?`

Options

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

Answer

C

Explanation

Given expression`=(2xx((1)/(sqrt(3)))^(2)*sec^(2)52^(@)sin^(2)(90^(@)-52^(@)))/("cosec"^(2)70^(@)-tan^(2)(90^(@)-70^(@)))=(2)/(3)*(sec^(2)52^(@)cos^(2)52^(@))/(("cosec"^(2)70^(@)-cot^(2)70^(@)))`
`=(2)/(3)xx(1)/(1)=(2)/(3).`