त्रिकोणमितीय तालिका का प्रयोग किये बिना निम्न का मान ज्ञात कीजिए-

`(-tan thetacos (90^(@)-theta)+sec thetacosec (90^(@)-theta)+sin^(2)35^(@)+sin ^(2)55^(@))/(tan 10^(@)tan20^(@)tan 30^(@)tan 70^(@)tan 80^(@))`

Explanation

यहाँ `(-tan thetacot (90^(@)-theta)+sec thetacosec (90^(@)-theta)+sin ^(2)35^(@)+sin ^(2)55^(@))/(tan 10^(@)tan 20^(@)tan 30^(@)tan70^(@)tan80^(@))`
`=(-tan^(2)thetatantheta+sec theta sec theta+sin ^(2)35^(@)+sin^(2)(90^(@)-35^(@)))/(tan 10^(@)tan 20^(@)tan30^(@)tan (90^(@)-20^(@))tan (90^(@)-10^(@)))`
`=(-tan ^(2)theta+sec ^(2)theta+sin ^(2)35^(@)+cos ^(2)35^(@))/(tan10^(@)tan20^(@)tan30^(@)cot20^(@)cot10^(@))`
`=((sec ^(2)theta-tan^(2)theta)+(cos ^(2)35^(@)+sin^(2)55^(@)))/((tan 10^(@)theta-tan^(2)theta)+(cos ^(2)35^(@)+sin^(2)35^(@)))=(1+1)/(1+1xx(1)/(sqrt3))=2sqrt3.`