this is a trigonometric identity:. your goal is to verify/prove the identity by manipulating one...

This is a trigonometric identity: cosθ secθ =1

This is a trigonometric identity: cosθ secθ =1

Your goal is to verify/prove the identity by manipulating one side of the equation until it looks like the other side.

This is a trigonometric identity: cosθ secθ =1

Your goal is to verify/prove the identity by manipulating one side of the equation until it looks like the other side.

cosθ1

cosθ=1

According to trig. ratios, you can rewrite secθ as 1

cosθ

This is a trigonometric identity: cosθ secθ =1

Your goal is to verify/prove the identity by manipulating one side of the equation until it looks like the other side.

cosθ1

cosθ=1

By multiplying, you will get:

cosθcosθ

=1

According to trig. ratios, you can rewrite secθ as 1

cosθ

This is a trigonometric identity: cosθ secθ =1

Your goal is to verify/prove the identity by manipulating one side of the equation until it looks like the other side.

cosθ1

cosθ=1

By multiplying, you will get:

cosθcosθ

=1

1=1

According to trig. ratios, you can rewrite secθ as 1

cosθ

This is a trigonometric identity: cosθ secθ =1

Your goal is to verify/prove the identity by manipulating one side of the equation until it looks like the other side.

cosθ1

cosθ=1

By multiplying, you will get:

cosθcosθ

=1

1=1

According to trig. ratios, you can rewrite secθ as 1

cosθ

You just verified the identity.

So, Verification Format Looks like this:

cosθ secθ =1

cosθ1

cosθ=1

cosθcosθ

=1

1=1

Now let’s look at another one in proof format:

Prove:cscθsecθ

=cotθ

cscθsecθ

1 1Given

cscθsecθ

=

1sinθ1

cosθ

2cscθsecθ

1 1Given

cscθsecθ

=

1sinθ1

cosθ

2cscθsecθ

1 1Given

2 Trig. Ratios

cscθsecθ

=

1sinθ1

cosθ

2cscθsecθ

1 1Given

2 Trig. Ratios

3

cscθsecθ

=

1sinθ1

cosθ

2cscθsecθ

1 1Given

2 Trig. Ratios

3 3Division of Fractions

cscθsecθ

=

1sinθ1

cosθ

2cscθsecθ

1 1Given

2 Trig. Ratios

3 3Division of Fractions

1

sinθ•cosθ1

=cosθsinθ

4

cscθsecθ

=

1sinθ1

cosθ

2cscθsecθ

1 1Given

2 Trig. Ratios

3 3Division of Fractions

1

sinθ•cosθ1

=cosθsinθ

4 4Multiplication

Multiplication4cosθsinθ

=cotθ51

sinθ•cosθ1

=cosθsinθ

4

cosθsinθ

=cotθ51

sinθ•cosθ1

=cosθsinθ

4 Multiplication45Trig. Ratios

cosθsinθ

=cotθ51

sinθ•cosθ1

=cosθsinθ

4 Multiplication45Trig. Ratios

“See.................You can do a Trig. Proof”

cosθsinθ

=cotθ51

sinθ•cosθ1

=cosθsinθ

4 Multiplication45Trig. Ratios

“See.................You can do a Trig. Proof”

If you are asked to verify, just show the steps.

cosθsinθ

=cotθ51

sinθ•cosθ1

=cosθsinθ

4 Multiplication45Trig. Ratios

“See.................You can do a Trig. Proof”

If you are asked to verify, just show the steps.

If you are asked to prove, include the reasons for each step.

cosθsinθ

=cotθ51

sinθ•cosθ1

=cosθsinθ

4 Multiplication45Trig. Ratios

“See.................You can do a Trig. Proof”

If you are asked to verify, just show the steps.

If you are asked to prove, include the reasons for each step.

That’s It !