Write cos 551° + cos 101° as a product of two trigonometric functions and simplify, if possible.?

Question

Honestly I don't know where to start with this.

Answer 1

Using sum and product rule of trigonometry,

cos C+ cos D =2 cos (C+D/2) cos (C-D/2)

Substitute 551 for C  and 101 for D.

cos 551+ cos 101 =2 cos (551+101/2) cos (551-101/2)

                                 =2 cos (652/2) cos (450/2)

                                  =2 cos (326) cos (225)

                                 =2 cos(360-34)cos(180+45)

                                  =2 cos34 *(-cos45)

                                  =-2cos34 cos45

                                  =-1.172