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The differential coefficient of sin^(-1)...

The differential coefficient of `sin^(-1)((5cos x-4s in x)/(sqrt(41)))` is `-2` b.`-1` c. `1` d. `2`

A

`-2`

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Let `u=sin^(-1)((4)/(5)sin2x+(3)/(5)cos2x)=sin^(-1)sin(alpha+2x).`
where `sin alpha=(3)/(5), cos alpha=(4)/(5)`
i.e., `u=alpha+2x.`
Similary, `y=cos^(-1)((5cos x-4 sinx)/(sqrt(41)))`
`=cos^(-1)cos(beta+x),`
Here, `cos beta=(5)/(sqrt(41)), sin beta=(4)/(sqrt(41))`
i.e., `v=beta+x`
`therefore" "(du)/(dv)=((du)/(dx))/((dv)/(dx))=(2)/(1)=2.`
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