Find `(dy)/(dx)` for the function: `y=(log)_esqrt((1+sinx)/(1-sinx)),w h e r ex=pi/3`

Answer

2

Explanation

`y=log sqrt((1+ sin x)/(1- sin x))=(1)/(2)[log_(e)(1+ sin x) -log _(e) (1- sin x)]`
`therefore" "(dy)/(dx)=(1)/(2){(1)/(1+ sin x dx)(d)/(dx)(1+ sin x)-(1)/(1- sin x )(d)/(dx)(1- sin x )}`
`=(1)/(2){(cos x)/(1+ sin x)+(cos x )/(1-sin x)}`
`=(1)/(2)cos x ((2)/(1- sin^(2)x))=(cos x)/(cos^(2)x)=sec x`
`"or "(dy)/(dx):|_(x=(pi)/(3))=sec""(pi)/(3)=2`