a) \(\sin {75^0} + \cos {75^0} = \sin ({45^0} + {30^0}) + \cos ({45^0} + {30^0}) \)

\(= \sin {45^0}.\cos{30^0}+\cos {45^0}.\sin {30^0} + \cos {45^0}.\cos{30^0} - \sin {45^0}.\sin{30^0} \)

\(= {{\sqrt 2 } \over 2}(\cos{30^0} + \sin {30^0} + \cos{30^0} - \sin {30^0}) \)

\(= {{\sqrt 2 } \over 2}.2{{\sqrt 3 } \over 2} = {{\sqrt 6 } \over 2} \)

b) \(\tan {267^0} + \tan {93^0} = \tan ({267^0} - {360^0}) + \tan {93^0} \)

\(= \tan ( - {93^0}) + tan{93^0} = 0\)

c) \(\sin {65^0} + \sin {55^0} = 2\sin {{{{65}^0} + {{55}^0}} \over 2}\cos {{{{65}^0} - {{55}^0}} \over 2} \)

\(= 2\sin {60^0}\cos {5^0} = \sqrt 3 \cos {5^0} \)

d) \(\cos {12^0} - \cos {48^0} = - 2\sin {{{{12}^0} + {{48}^0}} \over 2}\sin {{{{12}^0} - {{48}^0}} \over 2} \)

\(= - 2\sin {30^0}\sin ( - {18^0}) = 2\sin {30^0}\sin {18^0} \)

\(= 2.{1 \over 2}\sin {18^0} = \sin {18^0} \)