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Prove that (tan 25^@-tan 35^@ +tan 85^...

Prove that `(tan 25^@-tan 35^@ +tan 85^@)/(tan 25^@ tan 35^@ tan 85^@)`= 3

Text Solution

Verified by Experts

Here, we will use,
`tanxtan(60^@-x)tan(60^@+x) = tan3x`
`tanx+tan(60^@+x)+tan(120^@+x) = 3tan3x`
Now,
`L.H.S. = (tan25^@ - tan35^@+tan85^@)/(tan25^@ tan35^@tan85^@)`
`= (tan25^@ + tan(180-35)^@+tan85^@)/(tan25^@ tan(60-25)^@tan(60+25)^@)`
`= (tan25^@ +tan85^@+tan 145^@)/(tan25^@ tan(60-25)^@tan(60+25)^@)`
`= (tan25^@ +tan(60+25)^@+tan(120+25)^@)/(tan25^@ tan(60-25)^@tan(60+25)^@)`
...
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