What is `sin105^(@)+cos105^(@)` equal to ?

Options

A. `sin50^(@)`
B. `cos50^(@)`
C. `(1)/(sqrt(2))`
D. 0

Answer

C

Explanation

`sin105^(@)+cos105^(@)`
`=sin(60^(@)+45^(@))+cos(60^(@)+45^(@))`
`=(sin60^(@).sin45^(@)+cos60^(@).cos45^(@))+(cos60^(@)cos45^(@)-sin60^(@)sin45^(@))`
`=(sqrt(3))/(2).(1)/(sqrt(2))+(1)/(2).(1)/(sqrt(2))+(1)/(2).(1)/(sqrt(2))-(sqrt(3))/(2).(1)/(sqrt(2))`
`=(2)/(2sqrt(2))=(1)/(sqrt(2))`