Trigonometric Identities and Expressions

The video tutorial explains how to prove a given trigonometric equation by transforming and simplifying the terms using trigonometric identities. The process involves rewriting the equation in terms of sine and cosine, simplifying the expression, and finally proving that the left-hand side equals the right-hand side.

What is the initial equation given in the problem?

• tan(θ) / (1 - c(θ)) + c(θ) / (1 - tan(θ)) = 1 - sec(θ) * cosec(θ)

• tan(θ) / (1 + c(θ)) + c(θ) / (1 + tan(θ)) = 1 + sec(θ) * cosec(θ)

• tan(θ) * (1 - c(θ)) + c(θ) * (1 - tan(θ)) = 1 + sec(θ) * cosec(θ)

• tan(θ) / (1 - c(θ)) + c(θ) / (1 - tan(θ)) = 1 + sec(θ) * cosec(θ)

How is tan(θ) expressed in terms of sine and cosine?

• cos(θ) / sin(θ)

• sin(θ) / cos(θ)

• 1 / cos(θ)

• 1 / sin(θ)

What is the expression for c(θ) in terms of sine and cosine?

• 1 / sin(θ)

• 1 / cos(θ)

• sin(θ) / cos(θ)

• cos(θ) / sin(θ)

What is the purpose of rewriting trigonometric functions in terms of sine and cosine?

• To make the calculation more complex

• To simplify the calculation

• To eliminate trigonometric functions

• To change the equation

What is the expression for sec(θ) in terms of sine and cosine?

• 1 / sin(θ)

• 1 / cos(θ)

• cos(θ) / sin(θ)

• sin(θ) / cos(θ)

What is the expression for cosec(θ) in terms of sine and cosine?

• cos(θ) / sin(θ)

• 1 / sin(θ)

• 1 / cos(θ)

• sin(θ) / cos(θ)

What common factor is taken from the terms in the expression?

• 1 / sin(θ) * cos(θ)

• sin(θ) * cos(θ)

• 1 / tan(θ)

• tan(θ)

What identity is used to simplify sin²(θ) + cos²(θ)?

• sin²(θ) + cos²(θ) = 2

• sin²(θ) + cos²(θ) = 1

• sin²(θ) + cos²(θ) = -1

• sin²(θ) + cos²(θ) = 0

What happens to the common factor sin(θ) - cos(θ) in the numerator and denominator?

• It is multiplied

• It is added

• It is canceled

• It is divided

What is the result of taking LCM in the expression sin(θ) - cos(θ)?

• sin²(θ) - cos²(θ)

• sin³(θ) - cos³(θ)

• sin(θ) - cos(θ)

• sin(θ) + cos(θ)