This is the basic and conceptual question from trigonometric ratios in which we have to prove that
tan²66° – cot²24° = 0, without using trigonometric tables
RS Aggarwal, Class 10, Chapter 12, question no 2(vi).
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LHS=tan²66°−cot²24°
=tan²66°−cot²(90−66)°
=tan²66°−tan²66°
=0=RHS