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The value of tan65^(@) - 2tan40^(@) is e...

The value of `tan65^(@) - 2tan40^(@)` is equal to -

A

`-tan 20^(@)`

B

`tan 20^(@)`

C

`tan 25^(@)`

D

`tan 40^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
`tan65^(@) - 2tan40^(@)`
`= (tan45^(@) + 20^(@)) - 2tan40^(@)`
`= (1 + tan20^(@))/(1 - tan20^(@)) - (4 tan^(2) 20^(@))/(1 - tan20^(@))`
`= ((1 + tan20^(@))^(2) - 4 tan 20^(@))/(1-tan^(2)20^(@))`
`= ((1 - tan20^(@))^(2))/(1-tan^(2)20^(@)) = (1-tan20^(@))/(1+tan20^(@))`
`= tan(45^(@) - 20^(@)) = tan25^(@)`
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