सिद्ध कीजिए कि `tan 5^(@)tan 25^(@)tan 30^(@)tan 65^(@)tan 85^(@)=(1)/(sqrt3)`

Explanation

L. H. S. `=tan 5^(@)tan 25^(@)tan 30^(@)tan 65^(@)tan 85^(@)`
`=(tan 5^(@)tan 85^(@))(tan 25^(@)tan 65^(@))tan 30^(@)`
`=[tan 5^(@)tan (90^(@)-5^(@))][tan 25^(@)tan (90^(@)-25^(@))]tan 30^(@)`
`=(tan 5^(@)cot 5^(@))(tan 25^(@)cot 25^(@))tan 30^(@)`
`=(tan 5^(@)xx(1)/(tan 5^(@)))(tan 25^(@)xx(1)/(tan 25^(@)))tan 30^(@)`
`=1xx1xx(1)/(sqrt3)=(1)/(sqrt3)=` R.H.S.