This is the basic and conceptual question from trigonometric ratios in which we have to prove that
cos^2 75° + cos^2 15° = 1, without using trigonometric tables
RS Aggarwal, Class 10, chapter 12, question no 2(v)
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LHS=cos²75°+cos²15°
=cos²75°+sin²(90−15)°
=cos²75°+sin²75°
=1=RHS