This is the basic and conceptual question from trigonometric ratios on complementary angles in which we have to show that
sin²48° + sin²42° = 1 without using trigonometric tables
RS Aggarwal, Class 10, chapter 12, question no 2(vii).
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LHS
=sin²48°+sin²42°
=sin²48°+sin²(90−48)°
=sin²48°+cos²48°
=1=RHS