Choose the correct answer in each of the following questions:
`(cos0^(@)+sin30^(@) +sin45^(@))(sin 90^(@) + cos60^(@)-cos45^(@))=?`

Options

A. `(5)/(6)`
B. `(5)/(8)`
C. `(3)/(5)`
D. `(7)/(4)`

Answer

D

Explanation

`(cos0^(@)sin30^(@)+sin45^(@))(sin90^(@)+cos60^(@)-cos45^(@))`
`=(1+(1)/(2)+(1)/(sqrt(2)))(1+(1)/(2)-(1)/(sqrt(2)))=((3)/(2)+(1)/(sqrt(2)))((3)/(2)-(1)/(sqrt(2)))=((9)/(4)-(1)/(2))=(7)/(4).`