Question

Are there any other values of a such that the linearization of sin(x) at a = the linearization of tan(x) at a? Describe them through proof if they exist. If they don't exist, proove that instead.

Answer 1

FIrst, write down the linearization for both functions, using

\[ f_{a1}(x) \approx f_1(a)+ f_1'(a)(x-a) \\ f_{a2}(x) \approx f_2(a)+ f_2'(a)(x-a)\]
then equate terms
\[ f_1(a) = f_2(a) \\ f_1'(a) = f_2'(a) \]
and solve for a

Answer 2

how do you solve for a?