सिद्ध कीजिए : `(sin 135^(@)-cos 120^(@))/(sin 135^(@)+cos 120^(@))=3+2sqrt(2)`.

Explanation

`L.H.S. = (sin 135^(@)-cos 120^(@))/(sin 135^(@)+cos 120^(@))=((1)/(sqrt(2))-(-(1)/(2)))/((1)/(sqrt(2))+(-(1)/(2)))`
`((1)/(sqrt(2))+(1)/(2))/((1)/(sqrt(2))-(1)/(2)) =(sqrt(2)+1)/(sqrt(2)-1)=(sqrt(2)+1)/(sqrt(2)-1)xx(sqrt(2)+1)/(sqrt(2)+1)`
`=(2+1+2sqrt(2))/(2-1)=3+2sqrt(2)=R.H.S. " "` इति सिद्धम्