cos sin tan 既野...數學勁既請入

example like first question,
start for the complicated part, which is the left hand side,
(sec x - cos x)/sec x
= ( (1/cos x) - cos x ) / (1/cos x)
= ( (1-cos^2) / cos x) / (1/cos x)
by definition, 1-cos^2 x = sin^2 x
= (sin^2 x/ cos x) / (1/cos x)
= sin^2 x

question 2,
tan x + cot x = sinx cos x
at the left hand side,
sin x / cos x + cos x / sin x
= sin^2/ sin x cos x + cos^2 / sinx cos x
= 1 / sinx cos x
then second question is not identity

basically, u need to transform all tan, cot, csc, and sec become sin and cos. that makes life better.. =)