Mathematics

Problem

Answer the questions related to the Pythagorean identity. a. (i) Explain why

\tan x

is undefined when

\cos x=0

. b. (ii) Starting from the identity

\sin^{2}x+\cos^{2}x=1

, derive the identity

1+\tan^{2}x=\sec^{2}x

, clearly stating the restrictions on

x

for which the result is valid.