Verifying Trig Advanced Strategies

• Pythagorean ID on bottom 

• Rewrite using  reciprocal ID

•  Combine like terms on top

• Common Denominator (also the conjugate)

Simplify this set of conjugates (Hint: you will need to FOIL first)

• sinθ

• cot²θ

• tan²θ

• cos²θ

• 1

• Replace using Pythagorean ID

• Simplify (cancel)

•  Get a common denominator

• Put in terms of sine and cosine (reciprocal ID) 

• Simplify/cancel on top only

• Simplify (cancel)

• Simplify/cancel on top only

• Put in terms of sine and cosine (reciprocal ID) 

•  Get a common denominator

• Replace using Pythagorean ID

What could be our first strategy to simplify the right side?

• Rewrite into sines and cosines

• Combine fractions

• factor common factor

• multiply by the conjugate

• Use a Pythagorean Identity

What could be our first strategy to simplify the left side?

• Rewrite into sines and cosines

• separate fractions

• factor common factor

• multiply by the conjugate

• Use a Pythagorean Identity

What could be our first strategy to simplify the left side?

• Rewrite into sines and cosines

• separate fractions

• factor common factor

• multiply by the conjugate

• Use a Pythagorean Identity