The sum is equal to

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The sum 1sin⁡45∘sin⁡46∘+1sin⁡47∘sin⁡48∘+1sin⁡49∘sin⁡50∘+⋯+1sin⁡133∘sin⁡134∘\frac{1}{\sin45^\circ\sin46^\circ}+\frac{1}{\sin47^\circ\sin48^\circ}+\frac{1}{\sin49^\circ\sin50^\circ}+\cdots+\frac{1}{\sin133^\circ\sin134^\circ} is equal to (1) sec⁡(1∘)\sec(1^\circ) (2) csc⁡(1∘)\csc(1^\circ) (3) cot⁡(1∘)\cot(1^\circ) (4) None of these

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