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Unit 7 Lesson 2 Investigation 2

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Unit 7 Lesson 2 Investigation 2

Proving Trigonometric Identities

Reciprocal IdentitiesQuotient IdentitiesPythagorean Identities

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

From the last slide:

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

Here is another example:

We will start by working on the

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

Now we can cross cancel inside the parenthesis

Inside the brackets we need a common denominator

Next, we combine the fraction

Again we can cross cancel sinx

and we are left with…

Which equals the right side!

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.

Multiply the denominator (hint: use foil)

Use the Pythagorean indentify to simplify the denominator

Distribute the numerator:

Separate the fraction:

Reduce the fractions:

Next, simplify each fraction

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