Question

Use fundamental identities​ and/or the complementary angle theorem to find the exact value of the expression. do not use a calculator. tangent 30 degrees minus startfraction cosine 60 degrees over cosine 30 degrees endfraction

Answer 1

The given expression is

`tan 30 - (cos 60)/(cos30)`

And using complementary identity, which is

`cos(90- \theta) = sin \theta`

So we will get

`cos 60 = cos(90-30)=sin 30`

Substituting sin 30 for cos 60 in the given expression

`tan 30 - (sin 30)/(cos 30) \\ = tan 30- tan 30 \\ = 0`

So the value of the expression is 0.