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The value of sin^(-1)((3)/(5))+tan^(-1)(...

The value of `sin^(-1)((3)/(5))+tan^(-1)((1)/(7))` is equal to

A

0

B

`(pi)/(4)`

C

`(pi)/(3)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B

`sin theta = (3)/(5)`
`tan theta = (3)/(4)`
`=tan^(-1)((3)/(4))+tan^(-1)((1)/(7))`
`=tan^(-1)(((3)/(4)+(1)/(7))/(1-(3)/(4).(1)/(7)))`
`=tan^(-1)(((21+4)/(28))/((28-3)/(28)))`
`=tan^(-1)((25)/(25))=tan^(-1)(1)=(pi)/(4)`.
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