Verifying Trigonometric Identities

The video tutorial covers verifying trigonometric identities using half-angle formulas. It begins with proving that sine squared x/2 equals a specific expression involving cosecant and cotangent. The tutorial then moves on to proving a cosine squared identity by manipulating trigonometric expressions. Finally, it verifies a tangent identity using a specific form of the tangent half-angle formula. Each section involves algebraic manipulation and substitution to demonstrate the validity of the identities.

What is the main focus of the initial section of the video?

• Deriving the Pythagorean identity

• Graphing trigonometric functions

• Solving quadratic equations

• Introduction to verifying identities using half angle formulas

Which identity is used to verify sine squared x over 2?

• 1 + sine x divided by 2

• 1 - cosine x divided by 2

• 1 - sine x divided by 2

• 1 + cosine x divided by 2

What operation is performed to eliminate the radical in the sine identity?

• Multiplying by cosine

• Dividing by sine

• Squaring both sides

• Taking the square root

What is the result of multiplying the expression by one over sine x?

• Secant and tangent terms

• Tangent and cotangent terms

• Cosecant and cotangent terms

• Sine and cosine terms

What is the formula used for cosine squared x over 2?

• Square root of 1 minus cosine x divided by 2

• Square root of 1 minus sine x divided by 2

• Square root of 1 plus cosine x divided by 2

• Square root of 1 plus sine x divided by 2

How is the expression simplified in the cosine identity verification?

• By multiplying by sine over cosine

• By adding cosine to both sides

• By dividing by tangent

• By subtracting sine from both sides

Which form of tangent theta over two is chosen for the identity verification?

• Cosine theta divided by 1 plus sine theta

• Secant theta divided by 1 plus tangent theta

• Sine theta divided by 1 plus cosine theta

• Tangent theta divided by 1 plus secant theta

What is the purpose of multiplying by one over cosine in the tangent identity?

• To convert cosine into secant

• To convert secant into cosine

• To convert sine into tangent

• To convert tangent into sine

What is the final result of the tangent identity verification?

• Cosine x divided by sine x plus one

• Sine x divided by cosine x plus one

• Tangent x divided by secant x plus one

• Secant x divided by tangent x plus one

What is the key step in verifying the tangent identity?

• Distributing one over cosine

• Adding sine to both sides

• Multiplying by tangent

• Subtracting cosine from both sides