The value of `(sin90^(@)-cos45^(@)+cos60^(@))(cos0^(@)+sin45^(@)+sin30^(@))` is

Options

A. `(7)/(4)`
B. `(5)/(4)`
C. `(3)/(4)`
D. `(3)/(2)`

Answer

a

Explanation

According to the question,
`rArr(sin90^(@)-cos45^(@)+cos60^(@))`
`(cos0^(@)+sin45^(@)+sin30^(@))`
`rArr (1-(1)/sqrt(2)+(1)/(2))(1+(1)/sqrt(2)+(1)/(2))`
`rArr((3)/(2)-(1)/sqrt(2))((3)/(2)+(1)/sqrt(2))`
`rArr(9)/(4)-(1)/(2)`
`rArr(7)/(4)`