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The value of the expression log10(tan6^@...

The value of the expression `log_10(tan6^@)+log_10(tan12^@)+log_10(tan18^@)+...+log_10(tan84^@)` is

A

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`E=log_10(tan6^@)+log_10(tan12^@)+log_10(tan18^@)+...+log_10(tan84^@)`
`=log_10((tan6^@xxtan84^@)(tan12^@xxtan78^@)...(tan42^@xxtan48^@))`
`=log_10((tan6^@xxcot6^@)(tan12^@xxcot12^@)...(tan42^@xxtan42^@))`
`=log_10 1=0`
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