Question

Write the paranetric functions x=tant and y=sect in form y=f(x) by eliminating t

Answer 1

we know that sec^2t - tan^2t=1
x^2=tan^2t
y^2=sec^2t
y^2-x^2= sec^2t - tan^2t
y^2-x^2=1
y^2=1+x^2
y=(1+x^2)^(1/2)

Answer 2

\[1 + \tan^{2} t= \sec^{2} t\]

\[1 + x^{2} = y^{2} \]

\[\implies y = \sqrt{1 + x^{2}}\]