Question

Find the equation of the tangent to the curve y=sec x at the point (0 , 1). ​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{curve is y=secx}$

$\underline{\textsf{To find:}}$

$\textsf{The equation of the tangent to the curve at (0,1)}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{y=sec\,x}$

$\textsf{Differentiate with respect to x}$

$\mathsf{\dfrac{dy}{dx}=secx\,tanx}$

$\textsf{Slope of tangent:}$

$\mathsf{m=(\dfrac{dy}{dx})_(0,1)}$

$\mathsf{m=sec0\,tan0}$

$\mathsf{m=1{\times}0=0}$

$\textsf{The equation of tangent at (0,1) is}$

$\mathsf{y-y_1=m(x-x_1)}$

$\mathsf{y-1=0(x-0)}$

$\implies\boxed{\mathsf{y-1=0}}$

$\underline{\textsf{Answer:}}$

$\textsf{The equation of tangent is y-1=0}$