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Question
The value of tan1° tan2° tan3° ... tan89° is ______.
Options
0
1
`1/2`
Not defined
Solution
The value of tan1° tan2° tan3° ... tan89° is 1.
Explanation:
tan1° tan2° tan3°… tan89°
= tan1° tan2° … tan45° tan(90° - 44°) tan(90° - 43°) ..…tan(90° - 1°)
= tan1° tan2° … tan45° cot44° cot43° … cot1° ......[∵ tan(90° - θ) = cotθ]
= tan1° cot1° tan2° cot2°…tan45°… tan89° cot89°
= 1.1….1
= 1
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