त्रिकोणमितीय सारणी का प्रयोग किये बिना मान ज्ञात कीजिए :
`(cosec^(2)(90^(@)-theta)-tan^(2)theta)/(4(cos^(2) 48^(@)+cos^(2)42^(@)))-(2 tan^(2) 30^(@) sec^(2) 52^(@) sin^(2) 38^(@))/((cosec^(2)70^(@)-tan^(2) 20^(@)))`

Explanation

`(cosec^(2)(90^(@)-theta)-tan^(2)theta)/(4(cos^(2) 48^(@)+cos^(2)42^(@)))-(2 tan^(2) 30^(@) sec^(2) 52^(@) sin^(2) 38^(@))/((cosec^(2)70^(@)-tan^(2) 20^(@)))`
`=(sec^(2)theta-tan^(2)theta)/(4{cos^(2)(90^(@)-42^(@))+cos^(@)42^(@)})-(2((1)/(sqrt(3)))sec^(2) (90^(@)-38^(@)) sin^(2)38^(@))/(cosec^(2) (90^(@) -20^(@))-tan^(2) 20^(@))`
` = (1)/4(sin^(2) 42^(@) + cos^(2) 42^(@)) - (2cosec^(2)38^(@) * sin^(2) 38^(@))/(3{sec^(2) 20^(@) - tan^(2) 20^(@)})`
`=(1)/(4)-(2cosec^(2)38^(@)xx(1)/(cosec^(2)38^(@)))/(3)=(1)/(4)-(2)/(3)=(-5)/(12)`