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Question
Write the value of tan1° tan 2° ........ tan 89° .
Solution
Tan 1° tan 2° … tan 89°
= tan 1° tan 2° tan 3° … tan 45° … tan 87° tan 88° tan 89°
= tan 1° tan 2° tan 3° … tan 45° … cot(90° − 87° ) cot(90° − 88° ) cot(90° − 89° )
= tan 1° tan 2° tan 3° … tan 45° … cot 3° cot 2° cot 1°
`= tan 1° × tan 2° × tan 3° × …× 1 × …× 1/( tan 3° )xx 1/ (tan 2°) xx 1/ (tan 1°)`
= 1
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