Consider the function

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

y = \sec x

, defined for all

x

in its domain. (a) Rewrite

y

entirely in terms of the cosine function. (b) Differentiate the expression obtained in part (a) with respect to

x

, leaving your answer in terms of

\sin x

and

\cos x

only. (c) Show algebraically that the result from part (b) is equivalent to

\sec x\tan x

. Clearly justify each step in your simplification.