Simplify, using trigonometric tables

sin 30°30’+cos 40°20’

First consider sin 30° 30’,

The relevant part of the sine table is given below.

From the table, we have

Sin 30° 30’ = 0.5075

Then consider cos 40° 20’,

We write cos 40° 20’ = cos 40° 18’ + 2’.

The relevant part of the cosine table is given below.

From the table, we have

cos 40° 18’ = 0.7627

Mean difference for 2’ = 0.0004

We know that mean difference is to be subtracted in the case of cosine.

∴ cos 40° 20’ = 0.7627 - 0.0004 = 0.7623

∴ sin 30° 30’ + cos 40° 20’ = 0.5075 + 0.7623 = 1.2698