यदि `tan{cos^(-1)(4/5) + tan^(-1)(2/3)}` का आंकिक मान `a/b` हो , तब
`b` का मान होगा

Options

A. `6`
B. `5`
C. `8`
D. `10`

Answer

A

Explanation

माना `cos^(-1)(4/5)= alpha`
` rArr cos alpha= 4/5`
` :. tan alpha = 3/4`
अब `tan{cos^(-1)(4/5)+tan^(-1)(2/3)}`
` = tan(alpha + tan^(-1). 2/3)`
` = (tan alpha+ 2/3)/(1 - tan alpha* 2/3) = 17/6 = a/b` , [दिया है ]
अतः a = 17 तथा b = 6