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Question

tan1.tan2.tan3...tan89=_________.


A
1
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B
tan 90
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C
3
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Solution

The correct option is B 1
Given, tan1.tan2.tan3.....tan44.tan45.tan46....tan89
[tanθ=cot(90θ)]
tan1.tan2.tan3.....tan44.tan45.tan46.....tan89= tan1.tan2.tan3.....tan44.tan45.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

Mathematics

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