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Unit 7 Lesson 2 Investigation 2. Proving Trigonometric Identities. Page 465 from the C+4B Text. Reciprocal Identities Quotient Identities Pythagorean Identities. Let’s start off with an easy example:. We will make the left side look like the right first by using the Pythagorean identity.

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unit 7 lesson 2 investigation 2

Unit 7 Lesson 2 Investigation 2

Proving Trigonometric Identities

page 465 from the c 4b text
Page 465 from the C+4B Text

Reciprocal IdentitiesQuotient IdentitiesPythagorean Identities

let s start off with an easy example
Let’s start off with an easy example:

We will make the left side look like the right first by using the Pythagorean identity

Next, we will re-write tan using the quotient identity

slide4

From the last slide:

We will finish by reducing cosine and both sides will now be identical.

slide6

We will start by working on the

left side of the equation by rewriting the sine and cosine using the quotient identity:

slide7

Now we can cross cancel inside the parenthesis

Inside the brackets we need a common denominator

slide8

Next, we combine the fraction

Again we can cross cancel sinx

and we are left with…

Which equals the right side!

slide9

Here is another example:

Let’s start by working on the right side of the equation by multiplying by 1

in the conjugate of the denominator.

slide10

Multiply the denominator (hint: use foil)

Use the Pythagorean indentify to simplify the denominator

slide11

Distribute the numerator:

Separate the fraction:

Reduce the fractions:

slide12

Next, simplify each fraction

The identity is now complete and so is the tutorial. See your teacher for practice problems.

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