The equation of tangent to the curve `y=2cos x` at `x=(pi)/4` is

Options

A. `y-sqrt(2)=2sqrt(2)(x-(pi)/4)`
B. `y+sqrt(2)=sqrt(2)(x+(pi)/4)`
C. `y-2sqrt(2)=-sqrt(2)(x-(pi)/4)`
D. `y-sqrt(2)=sqrt(2)(x-(pi)/4)`

Answer

C

Explanation

Given `y=2cosx`
At `x=x/4,y=2/(sqrt(2))=sqrt(2)`
and `(dy)/(dx)=-2 sin x`
`:.((dy)/(dx))_(x=pi//4)=-sqrt(2)`
`:.` Equation of tangent at `((pi)/4, sqrt(2))` is `y-sqrt(2)=-sqrt(2)(x-(pi)/4)`