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Question

Find the value
tan1.tan2.tan3..........tan89

A
1
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B
tan90
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C
3
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Solution

The correct option is A 1
tan1.tan2.tan3..........tan44.tan45.tan46.........tan89=tan1.tan2.tan3.....tan44.1.cot(9046)....cot(9089)=tan1.tan2.tan3.........tan44 cot44........cot2 cot1
Rearranging the terms,
= tan1 cot1.tan2cot2.tan2.cot3........tan44 cot44
Now, we know that tanθ=1cotθ
tanθ×cotθ=1
Thus,tan1.cot1.tan2cot2.tan2.cot3........tan44.cot44=1

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