सिध्द कीजिए कि : `(cos9^(@) + sin 9^(@))/(cos 9^(@) - sin 9^(@)) = tan 54^(@)`

Explanation

बायाँ पक्ष् `= (cos 9^(@) + sin 9^(@))/(cos 9^(@) - sin 9^(@))`
` = (cos 9^(@) + sin 9^(@))/(cos 9^(@) - sin 9^(@)) xx (cos 9^(@) + sin 9^(@))`
` = ((cos 9^(@)+ sin 9^(@))^(2))/((cos^(2)9^(@) - sin^(2)9^(@)))`
`=(cos^(2) 9^(@)+ sin^(2)9^(@) +2 sin 9^(@)cos 9^(@))/(cos^(2)9^(@) -sin^(2) 9^(@))`
` =(1+ sin 18^(@))/(cos 18^(@)) = (1+ cos 72^(@))/(sin 72^(@))`
`= (2 cos^(2) 36^(@))/(2 sin 36^(@) cos 36^(@)) = cot 36^(@) = tan 54^(@)`
= दायाँ पक्ष ।
अथवा
`(cos 9^(@) + sin 9^(@))/( cos 9^(@) - sin 9^(@)) = (1+ tan 9^(@))/(1- tan 9^(@)) ` अंश और हर में cos `9^(@)` से भाग देने पर
`= (tan 45^(@) + tan 9^(@))/(1- tan 45^(@) tan9^(@)) = tan (45^(@) + 9^(@))`
`= tan 54^(@) =` दायाँ पक्ष।