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.
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
We will finish by reducing cosine and both sides will now be identical.
left side of the equation by rewriting the sine and cosine using the quotient identity:
Inside the brackets we need a common denominator
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.
Use the Pythagorean indentify to simplify the denominator
Separate the fraction:
Reduce the fractions:
The identity is now complete and so is the tutorial. See your teacher for practice problems.