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The value of tan1^@tan2^@tan3^@...tan89^...

The value of `tan1^@tan2^@tan3^@...tan89^@` is

A

`0`

B

`1`

C

`(1)/(2)`

D

Not defined

Text Solution

Verified by Experts

The correct Answer is:
B
Given expression, `tan1^(@)tan2^(@)tan3^(@) ... tan89^(@)`
`=tan1^(@)tan2^(@)...tan45^(@)*tan(90^(@)-44^(@))tan(90^(@)-43^(@))...tan(90^(@)-1^(@))`
`=tan1^(@)*cot1^(@)*tan2^(@)*cot2^(@)...tan89^(@)*cot89^(@)`
`1*1...1*1=1`
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