Question

The value of cos57+sin27 is​

Answer 1

Answer:   cos 3°

Step-by-step explanation:

= cos 57 - cos ( 90 - 27)                         ...........( sin A = cos (90-A)

= cos 57 - cos 63

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

= 2 cos (57 + 63 / 2) cos ( 57 - 63 / 2)

= 2 cos ( 120 / 2 ) cos (-6/2)

= 2 cos (60) cos ( - 3)

= 2 cos 60 cos 3                                      .............( cos ( - A) = cos A )

=  2 x 1/2 x cos 3°

= cos 3°