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SMO 2021 Senior Round 1 Question 19

SMO · SMO 2021 Senior Round 1

Question 19

Find the value of $$\frac1{\sin^2 0.5^\circ}-\tan^2 0.5^\circ+\frac1{\sin^2 1.5^\circ}-\tan^2 1.5^\circ+\frac1{\sin^2 2.5^\circ}-\tan^2 2.5^\circ+\cdots+\frac1{\sin^2 179.5^\circ}-\tan^2 179.5^\circ.$$