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"sin"^(-1)(4)/(5)+2"tan"^(-1)(1)/(3) is ...

`"sin"^(-1)(4)/(5)+2"tan"^(-1)(1)/(3)` is equal to

A

`(pi)/(3)`

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
C
`"sin"^(-1)(4)/(5)+2"tan"^(-1)(1)/(3)+"sin"^(-1)(4)/(5)`
`+"tan"^(-1)(2((1)/(3)))/(1-((1)/(3))^(2))`
`="sin"^(-1)(4)/(5)+"tan"^(-1)(3)/(4)`
`="sin"^(-1)(4)/(5)+"cos"^(-1)(4)/(5)=(pi)/(2)`
`[because"sin"^(-1)x+cos^(-1)x=(pi)/(2)]`
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