If `x=sin70^(0). sin50^(0)and y = cos60^(@). cos80^(0)`, then what is xy equal to ?

Options

A. `1//16`
B. `1//8`
C. `1//4`
D. `1//2`

Answer

A

Explanation

`x=sin70^(@).sin50^(@)andy=cos60^(@).cos80^(@)`
`rArrxy=cos60^(@).sin70^(@).sin50^(@).cos80^(@)`
`xy=(1)/(2).sin(90-20)*sin(90-40)*cos80`
`rArrxy=(1)/(2)*cos20*cos40*cos80`
`(becausesin(90-x)=cosx)`
`rArrxy=(1)/(2)*cos20^(@).cos(60-20)^(@).cos(60+20)^(@)`
`rArrxy=(1)/(2)[(1)/(4)"cos"3(20^(@))]=(1)/(2)xx(1)/(4)xxcos60^(@)=(1)/(16)`.
`[becausecostheta*cos(60-theta)*cos(60+theta)=(1)/(4)cos3theta]`