This is the basic and conceptual question from trigonometric ratios on complementary angles in which we have been asked to show that
sin53°cos37° + Cos53°sin37° = 1 without using trigonometric tables
RS Aggarwal, class 10, chapter 12, question no 3(i)
LHS = sin53° cos37° + cos53° sin37° = sin53°cos(90° – 53°) + cos53°sin(90° – 53°)
= sin53°sin53° + cos53°cos53°
= sin²53° + cos²53°
= 1 = RHS