Page 465 from the C+4B Text Reciprocal IdentitiesQuotient IdentitiesPythagorean 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 Next, we will re-write tan using the quotient identity

We will finish by reducing cosine and both sides will now be identical. From the last slide:

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!

Let’s start by working on the right side of the equation by multiplying by 1 in the conjugate of the denominator. Here is another example:

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.