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Find the value of tan22.5^(@)...

Find the value of `tan22.5^(@)`

Text Solution

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Let A `=22.5^(@)` and `tan 22.5^(@) = x`
Now, `2A=45^(@)`
We know that, `tan2A = (2tanA)/(1-tan^(2)A)`
`rArr 1=(2x)/(1-x^(2))`
`rArr x^(2) + 2x-1=0`
`rArr x=-1+-sqrt(2)`
`rArr x=sqrt(2)-1` [Since `x gt 0`]
`rArr tan22.5^(@)=sqrt(2)-1`
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