Without using trigonometric tables, prove that:
cosec2 72° - tan2 18° = 1

Consider cosec2 72° - tan2 18° = cosec2 72° - tan2 (90 - 72)°

= cosec2 72° - cot2 72°


= 1


(1 + cot2 θ = cosec2 θ cosec2 θ - cot2 θ = 1 )


Hence, proved.


2