यदि `sin A = 1/3`,तब `cos A. cosec A + tan A. sec A`का मान ज्ञात करें ।

Explanation

हम एक समकोण `Delta ABC` खींचते है , जिसमें `angleB = 90^(@)" और" BC = p = 1 , AC = h = 3`
अब ,`AB = sqrt(AC^(2)-BC^(2)) = sqrt((3)^(2)-(1)^(2)) = sqrt(9-1) = sqrt8 = 2sqrt2`
` :. cos A = b/h = (AB)/(AC) = (2sqrt2)/3 , cosec A = h/p = (AC)/(BC) = 3/1 = 3`
`tan A = p/b = (BC)/(AB) = 1/(2sqrt2) : sec A = h/b = (AC)/(AB) = 4/(2sqrt2)`
अब , `cos A . cosec A + tan A. sec A `
` = (2sqrt2)/3 xx 3 + 1/(2sqrt2) xx 3/(2sqrt2) = 2 sqrt2 + 3/8 = (16sqrt2+3)/8`