This is the basic and conceptual question from trigonometric ratios on complementary angles in which we have been asked to prove that
(sin65° + cos25°)(sin65° – cos25°) = 0
without using trigonometric tables
RS Aggarwal, Class 10, chapter 12, question no 2(ix)
LHS=(sin65°+cos25°)(sin65°−cos25°)
=sin²65°−cos²25°
=sin²65°−cos²(90−65)°
=sin²65°−sin²65°
=0=RHS