Trigonometric Identities and Formulas

The video tutorial covers verifying trigonometric identities using double angle formulas. It begins with an introduction to double angle formulas and proceeds to verify identities involving sine and cosine. The tutorial explains the use of double angle formulas for sine and cosine, including the verification of identities like sine plus cosine squared and cosine four x. It also covers the cosine of 3x identity using sum and difference formulas, emphasizing the importance of converting angles and using trigonometric identities effectively.

What is the result of squaring the sum of sine and cosine?

• Sine squared plus cosine squared

• Sine two theta plus one

• Two sine theta cosine theta

• One minus sine squared

How can sine 2 theta be expressed using tangent?

• Tangent squared theta minus one

• One minus tangent squared theta

• Sine squared theta plus cosine squared theta

• Two tangent theta divided by one plus tangent squared theta

What is the identity for one minus tangent squared?

• Cosine 2x divided by cosine squared x

• Cosine squared x divided by sine squared x

• Sine 2x divided by sine squared x

• Tangent 2x divided by tangent squared x

Which formula is used to reduce cosine 4x to a simpler form?

• Double angle formula

• Sum and difference formula

• Pythagorean identity

• Half angle formula

How many times do you need to apply the double angle formula to reduce 8x to 1x?

• Four times

• Three times

• Twice

• Once

What is the final expression for cosine 4x after applying the double angle formula twice?

• 2 cosine squared x minus 1

• 8 cosine to the fourth power of x minus 8 cosine squared plus 1

• 1 minus 2 sine squared x

• 4 cosine cubed x minus 3 cosine x

What is the formula for cosine of 3x?

• Cosine squared x minus sine squared x

• 2 cosine squared x minus 1

• 4 cosine cubed x minus 3 cosine x

• 1 minus 2 sine squared x

Which formula is used when dealing with an odd angle like 3x?

• Double angle formula

• Pythagorean identity

• Sum and difference formula

• Half angle formula

What is the result of applying the sum and difference formula to cosine 3x?

• Sine 2x times cosine x minus cosine 2x times sine x

• Cosine 2x times cosine x minus sine 2x times sine x

• Sine 2x times sine x plus cosine 2x times cosine x

• Tangent 2x times tangent x minus cosine 2x times cosine x

What is the expression for sine squared in terms of cosine?

• 1 plus cosine squared

• 2 cosine squared minus 1

• Cosine squared minus 1

• 1 minus cosine squared