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the value of tan9^@-tan2 7^@-tan6 3^@+ta...

the value of `tan9^@-tan2 7^@-tan6 3^@+tan8 1^@` is equal to

A

2

B

3

C

4

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
C
We have `tan 9^(@)-tan27^(@)-tan63^@)+tan81^(@)`
`=(tan9^(@)+tan81^(@))-(tan27^(@)+tan63^(@))`
`=(1)/(cos9^(@)cos81^(@))-(1)/(cows27^(@)-63^(@))`
`(1)/(sin9^(@)cos9^(@))-(1)/(sin27^(@)cos27^(@))`
`=(2)/(sin18^(@))-(2)/(sin54^(@))`
`=2[(sin54^(@)-sin18^(@))/(sin54^(@)sin18^(@))]`
`=2[(2cos36^(@)sin18^(@))/(sin18^(@)cos36^(@))]=4`
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