This is the basic and conceptual question from trigonometric ratios in which we have to prove that cosec^2 72° – tan^2 18° = 1 without using trigonometric tables.
RS Aggarwal, Class 10, chapter 12, question no 2(iv).
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LHS=cosec²72°−tan²18°
=cosec²72−tan²(90−72)°
=cosec²72°−cot²72°
=1=RHS