Find the value of

Answer

A, B, C, D

Explanation

(c) `2sin 45^(@) cos 15%(@)`
`sin C +sin D = 2 sin ((C +D)/(2)) cos ((C-D)/(2))`
`:. (C+D)/(2) = 45^(@)` or `C +D = 90^(@)` ...(i)
`(C-D)/(2) = 15^(@)` or `C-D = 30^(@)` ...(ii)
Solving these two equations, we get
`C = 60^(@), D = 30^(@)`
`:. 2 sin 45^(@) cos15^(@) = sin 60^(@) +sin 30^(@)`
`=((sqrt(3) +1)/(2))`
(d) Apply
`sin C - sin D = 2 sin ((C-D)/(2)) cos ((C +D)/(2))`
`C = 60^(@)` and `D = 30^(@)`
`:. 2 sin 15^(@) cos 45^(@) = sin 60^(@) - sin 30^(@)`
`:. 2sin 15^(@) cos 45^(@) = sin 60^(@) - sin 30^(@)`
`=((sqrt(3) -1)/(2))`