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Prove the following results: tan(cos^(...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`.
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