Question

Prove the following results: `tan(cos^(-1)4/5+tan^(-1)2/3)=(17)/6`
A. `13/6`
B. `17/6`
C. `19/6`
D. `23/6`

Answer 1

Correct Answer - B
`cos^(-1)x=tan^(-1)sqrt(1-16/25)/(4/5)=tan^(-1)3/4`.
`therefore cos^(-1)4/5+tan^(-1)2/3=tan^(-1)3/4+tan^(-1)2/3=tan^(-1)(3/4+2/3)/(1-3/4 xx 2/3)=tan^(-1)(3/4+2/3)/(1-3/4 xx 2/3) = tan^(-1)17/6`
`therefore` given exp. `=tan{tan^(-1)17/6}=17/6`
`therefore` given exp. `=tan{tan^(-1)17/6}=17/6`.