Question

20 POINTS

Verify which of the following are identities.
1) 8 cos theta tan theta csc theta=8

Answer 1

a) Only the first one is an identity.

Explanation:

1). 8 cos O tan O csc O = 8 simplifies to:

cos O tan O csc O = 1

cos O * (sin O / cos O) * (1 /sin O)

= cos O sin O / cos O sin O

= 1

So it is identity.

2) 13 sec^2 O/ cos^2 O - tan^2 O / cos^2O

= 13 sec^2 O - tan^2 O / cos^2 O

Now sec^2 O = 1 + tan^2 O, so we have:

(13( 1 + tan^2 O) - tan^2 O) / cos^2 O

= (12 tan^2 O + 13) / cos^2 O

This is not always = 2 so its not an identity.