Trigonometric Identities and Functions

This video tutorial explores the derivation of two new trigonometric identities using known identities. It begins with a review of basic identities like sine squared plus cosine squared equals one and tan X equals sine X over cosine X. The video then demonstrates how to derive the identities 1 + cot²x = csc²x and tan²x + 1 = sec²x by dividing both sides of the initial identity by sine squared and cosine squared, respectively. The importance of memorizing these identities for A-level courses is emphasized, and a method to easily derive one identity from another is shown.

What is the basic trigonometric identity involving sine and cosine?

• sine squared plus cosine squared equals one

• sine squared times cosine squared equals one

• sine squared plus cosine squared equals zero

• sine squared minus cosine squared equals one

How is tangent defined in terms of sine and cosine?

• Tangent is cosine over sine

• Tangent is sine over cosine

• Tangent is cosine minus sine

• Tangent is sine times cosine

What operation is performed on both sides of the equation to derive the first identity?

• Subtract sine squared

• Divide by sine squared

• Multiply by sine squared

• Add sine squared

What is the result of dividing sine squared X by itself?

• Cosine

• One

• Sine

• Zero

How can cosine over sine be expressed?

• Cosecant

• Secant

• Tangent

• Cotangent

What is the first identity derived in the video?

• 1 plus cot squared x equals csc squared x

• 1 plus tan squared x equals sec squared x

• 1 plus cot squared x equals sec squared x

• 1 plus cot squared x equals csc squared x

What operation is performed to derive the second identity?

• Subtract cosine squared

• Multiply by cosine squared

• Divide by cosine squared

• Add cosine squared

What is the result of dividing cosine squared X by itself?

• Tangent

• One

• Sine

• Zero

How can sine over cosine be expressed?

• Secant

• Cosecant

• Cotangent

• Tangent

What is the second identity derived in the video?

• 1 plus cot squared x equals csc squared x

• 1 plus tan squared x equals sec squared x

• 1 plus cot squared x equals sec squared x

• 1 plus tan squared x equals csc squared x