दिय गए चित्र से निम्नलिखित के मान ज्ञात करें :
(i) ` sin theta + sin alpha" "(ii) sec^(2) theta - tan ^(2) theta`

Explanation

समकोण `Delta CDE "में ," DE = sqrt(CE^(2)-CD^(2)) = sqrt(5^(2)-3^(2))=sqrt(25-9)=sqrt16 = 4`
` :. sin alpha = p/h = (DE)/(CE) = 4/5`
समकोण `Delta ABE "में," BE = CD = 3, AB = AC - BC = AC - ED = 8 - 4 = 4`
`:. AE = sqrt(AB^(2)+BE^(2)) = sqrt(4^(2)+3^(2)) = 5`
` :. Delta ABE " से ," sin theta = p/h = (BE)/(AE) = 3/5`
`sec theta = h/b = (AE)/(AB) = 5/4 , tan theta = p/b = (BE)/(AB) = 3/4`
(i) `sin theta + sin alpha = 3/5 + 4/5 = (3+4)/5 = 7/5`
(ii) ` sec^(2) theta - tan^(2) = (5/4)^(2) - (3/4)^(2) = 25/16 - 9/16 = (25-9)/16 = 16/16 = 1`.