`Delta ABC` "का " `angleB` समकोण है । यदि `tan A = 1/sqrt3`,तो , निम्नलिखित के मान बताइये :
`(i) sin A cos C + cos A sin C " "(ii)cos A cos C - sin A sin C `

Explanation

दिया है , `tan A = (BC)/(AB) = 1/sqrt3 :. BC : AB = 1 : sqrt3`
मान लीजिए B = k और `AB = sqrt3k `
अब , `AC = sqrt(AB^(2)+BC^(2))=sqrt((sqrt3k)^(2)+(k)^(2))` [ पाइथगोरस प्रमेय से ]
` = sqrt(3k^(2)+k^(2)) = sqrt(4k^(2))=2k`
अब समकोण `Delta ABC " से ," sin A = (BC)/(AC) = k/(2k) = 1/2`
` cos A = (AB)/(AC) = (sqrt3k)/(2k) = sqrt3/2`
` sin C = (AB)/(AC) = (sqrt3k)/(2k) = sqrt3/2 " और " cos C = (BC)/(AC) = k/(2k) = 1/2`
(i) `sin A cos C + cos A sin C = 1/2 * 1/2 + sqrt3/2 *sqrt3/2 = 1/4 + 3/4 = 1`
(ii) `cos A cos C - sin A sin C = sqrt3/2 * 1/2 - 1/2 * sqrt3/2 = sqrt3/2 = sqrt3/4 - sqrt3/4 = 0`.