The numerical value of
`(cos^(2)45^(@))/(sin^(2)60^(@))+(cos^(2)60^(@))/(sin^(2)45^(@))-(tan^(2)30^(@))/(cot^(2)45^(@))-(sin^(2)30^(@))/(cot^(2)30^(@))` is

Options

A. `3//4`
B. `1//4`
C. `1//2`
D. `1(1)/(4)`

Answer

a

Explanation

`(cos^(2)45^(@))/(sin^(2)60^(@))+(co^(2)60^(@))/(sin^(2)sin45^(@))-(tan^(3) 30)/(cot^(2)45)`
`(sin^(2)30)/(cot^(2)cot)`
`rArr(((1)/sqrt(3))^(2))/((sqrt(3)/(2))^(2))+((1)/(2))^(2)/(((1)/sqrt(2))^(2))-(((1)/sqrt(3)) ^(2))/(1)^(2)-(((1)/(2))^(2))/((sqrt(3))^2)`
`=(2)/(3)+(1)/(2)-(1)/(3)-(1)/(12)`
`=(1)/(3)+(1)/(2)-(1)/(12)`
`=(4+6-1)/(12)rArr(9)/(12)3//4`