# cos sin tan 既野...數學勁既請入

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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.. =)