सिद्ध करे कि
`4(cot^(-1) 3 + cosec^(-1)sqrt(5)) = pi`.

Explanation

माना कि
`cot^(-1) 3 =alpha, cosec^(-1) sqrt(5) =beta`
`rArr cot alpha =3` तथा `cosec beta = sqrt(5)`
`rArr tan alpha = (1)/(3)`
तथा `tan beta = (1)/(cotbeta) = (1)/(sqrt(cosec^(2)beta-1)) = (1)/(sqrt((5)^(2) -1))=(1)/(2)`
`rArr alpha =tan^(-1)""(1)/(3), beta = tan^(-1)""(1)/(2)`
अब, `L.H.S. = 4(alpha +beta) = 4(tan^(-1)""(1)/(3) +tan^(-1)""(1)/(2))`
`=4[tan^(-1)""((1)/(3)+(1)/(2))/(1-(1)/(3)*(1)/(2))] = 4tan^(-1) 1 = 4*(pi)/(4) = pi = R.H.S.`