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Question: \[\tan 1{^\circ}\tan 2{^\circ}\tan 3{^\circ}\tan 4{^\circ}........\tan 89{^\circ} =\]...

tan⁡1∘tan⁡2∘tan⁡3∘tan⁡4∘........tan⁡89∘=\tan 1{^\circ}\tan 2{^\circ}\tan 3{^\circ}\tan 4{^\circ}........\tan 89{^\circ} =

A

1

B

0

C

∞\infty

D

½

Answer

1

Explanation

Solution

tan⁡1∘tan⁡2∘....tan⁡89∘\tan 1{^\circ}\tan 2{^\circ}....\tan 89{^\circ}

=(tan⁡1∘tan⁡89∘)(tan⁡2∘tan⁡88∘)......=1×1×1....=1.= (\tan 1{^\circ}\tan 89{^\circ})(\tan 2{^\circ}\tan 88{^\circ})...... = 1 \times 1 \times 1.... = 1.