Advanced Examples 5-8

Advanced Examples

Verifying identities

Follow the slides to verify the identities, problems 5-8 (handout examples)

​Choose the most complex side of the equation to verify the identity.

Multiple Choice

5. Which side of the equation should we simplify?

• Left

• Right

Multiple Choice

What is a possible first step?

• Separate the fraction

• Use a Pythagorean identity

• Multiply by the conjugate

• Cancel the secant

Multiple Choice

How can we rewrite the expression?

• Use reciprocal identities.

  Cancel the secants to get 1

• Cross multiply

• Square the fractions

• Multiply everything by sine

​Can you see what your last step should be?

​Choose the most complex side of the equation to verify the identity.

Multiple Choice

6. Which side of the equation should we simplify?

• Left

• Right

Multiple Choice

What is the best possible first step?

• Use a Pythagorean identity

• separate the fractions

• Rewrite using reciprocal identities

• Factor the numerator

​Can you see what your last step should be?

​Choose the most complex side of the equation to verify the identity.

Multiple Choice

7. Which side of the equation should we simplify?

• Left

• Right

Multiple Choice

What is the best possible first step?

• Use a Pythagorean identity

• Expand the squared factor

• Rewrite using reciprocal identities

• Factor a common factor

​Can you see an identity after expanding?

Multiple Select

What are possible next steps?

• Multiply everything by sine

• Distribute tangent

• factor out the 2

• Rewrite tangent

  as sine/cosine

​What can we do after distributing and rewriting?

Can you see it?

​What can we do when simplifying the left side?

Multiple Choice

What could we do to rewrite the left side of the equation?

• Factor the numerator (difference of squares)

• Use a Pythagorean identity

• Keep change flip

• Multiply by the conjugate

Multiple Choice

How can we proceed?

• Separate as two fractions

• Rewrite the denominator

  (Pythagorean identity)