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Prove that (cos100sin10^0)/(cos10^0-s i...

Prove that `(cos100sin10^0)/(cos10^0-s in 10^0)=tan55^0`

Text Solution

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`(cos 10^(@)+sin10^(@))/(cos 10^(@)-sin10^(@))=(1+tan 10^(@))/(1-tan 10^(@))`
`=(tan 45^(@)+tan 10^(@))/(1-tan 45^(@)tan 10^(@))`
(dividing by `cos 10^(@)`)
`=tan (45^(@)+10^(@))=tan 55^(@)`.
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