If `sin^(-1)1 + "sin"^(-1)(4)/(5)=sin^(-1)x`, then what is x equal to?

Options

A. `3//5`
B. `4//5`
C. 1
D. 0

Answer

A

Explanation

Let `sin^(-1)(1)+sin^(-1)((4)/(5))=sin^(-1)x`
Let `sin^(-1)(1)= theta rArr sin theta =1 rArr cos theta = 0`
and `sin^(-1)((4)/(5))=phi rArr sin phi =((4)/(5))rArr cos phi = sqrt(1-(16)/(25))`
`=sqrt((9)/(25))=(3)/(5)`
`therefore sin^(-1)x = theta + phi`
`rArr x = sin(theta + phi)=sin theta cos phi + cos theta sin phi`
`=1xx(3)/(5)+0xx(4)/(5)`
`rArr x = (3)/(5)`