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Question

If tan1tan1tan2.........tan89=x28, then the value of x can be

A
1
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B
1
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C
3
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D
3
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Solution

The correct options are
B 3
C 3
Given tan1otan2otan3o..........tan87otan88otan89o=x28

tan1otan2otan3o..........tan87otan88otan89o

=(tan1otan89o)(tan2otan88o)...(tan44otan46o)tan45o
=(tan1otan(901)o)(tan2otan(902)o).......(tan44otan(9044)o)tan45o

we know that cotA=tan(90˚A)

=(tan1ocot1o)(tan2ocot2o).......(tan44ocot44o)tan45o=1

Hence, 1=x28x2=9x=±3

Therefore, Answer is 3 and 3

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