सिद्ध कीजिए कि ` sin(sin^(-1)""(1)/(3)+sec^(-1)3)+cos(tan^(-1)""(1)/(2)+tan^(-1)2)=1`

Options

A. 1
B. 2
C. 3
D. 4

Answer

A

Explanation

`sin[sin^(-1)((1)/(3))+sec^(-1)(3)]`
`+cos[tan^(-1)((1)/(2))+tan^(-1)(2)]`
`=sin[sin^(-1)((1)/(3))+cos^(-1)((1)/(3))]`
`+cos[tan^(-1)((1)/(3))+cot^(-1)((1)/(2))]`
`="sin"(pi)/(2)+"cos"(pi)/(2)`
`[because sin^(-1)x+cos^(-1)x=(pi)/(2)]=1`