Mastering Trigonometric Identities with Fractions

Anil Kumar's video series on trigonometry covers six trigonometric identities, focusing on fractions, tangent, and reciprocal trigonometric ratios. The video provides a list of formulas, including the Pythagorean identity, and demonstrates how to prove identities using these formulas. The tutorial progresses from simple to complex identities, offering strategies and techniques for solving them. The video emphasizes the importance of rationalization and manipulation in proving identities, providing step-by-step solutions and encouraging viewers to practice and learn from the examples.

Which of the following is a Pythagorean trigonometric identity?

• sec(x) = 1 / cos(x)

• tan(x) = sin(x) / cos(x)

• sin^2(x) + cos^2(x) = 1

• cot(x) = cos(x) / sin(x)

What is the simplified form of 1 - cos(x) / sin(x)?

• cot(x) - tan(x)

• cosec(x) - cot(x)

• tan(x) - sec(x)

• cosec(x) - sec(x)

How can tan^2(x) be expressed using sec(x)?

• sec(x) + 1

• sec^2(x) + 1

• sec(x) - 1

• sec^2(x) - 1

What is the common denominator used in the identity 4 sec(x) / (cosec(x) - 1) + cosec(x) / (cosec(x) + 1)?

• cosec^2(x) - 1

• sec^2(x) - 1

• (cosec(x) - 1)(cosec(x) + 1)

• (sec(x) - 1)(sec(x) + 1)

Which trigonometric identity is used to simplify 1 - sin^2(x)?

• cot^2(x)

• sec^2(x)

• tan^2(x)

• cos^2(x)

What is the result of rationalizing 1 + sin(x) by multiplying with 1 - sin(x)?

• 1 + cos^2(x)

• 1 - sin^2(x)

• 1 + sin^2(x)

• 1 - cos^2(x)

In the identity sec(x) - tan(x) whole square, what is the expanded form?

• sec^2(x) - tan^2(x)

• sec^2(x) - 2 sec(x) tan(x) + tan^2(x)

• sec^2(x) + tan^2(x)

• sec^2(x) + 2 sec(x) tan(x) + tan^2(x)

What is the simplified form of tan(x) sin(x) / (tan(x) + sin(x))?

• sin(x) / (1 + tan(x))

• cos(x) / (1 + sin(x))

• sin(x) / (1 + cos(x))

• tan(x) / (1 + sin(x))

How do you rationalize the expression 1 - cos(x) / sin(x)?

• Multiply by 1 + sin(x) / 1 + sin(x)

• Multiply by 1 - cos(x) / 1 - cos(x)

• Multiply by 1 - sin(x) / 1 - sin(x)

• Multiply by 1 + cos(x) / 1 + cos(x)

What is the final simplified form of 1 - cos(x) / sin(x) after rationalization?

• 1 - cos(x) / sin(x)

• sin(x) / 1 + cos(x)

• sin(x) / 1 - cos(x)

• 1 + cos(x) / sin(x)