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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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Pythagorean Identities

Intro

Concept Quizzes

Warmup
Derivation
Sine and Cosine
Further Identities
Problem Solving

Challenge Quizzes

Level 1
Level 2
Level 3
Level 4

Basic Proving Identities using Pythagorean Theorem

Which of the following is equal to \(1-\cos^2\theta?\)

\[\cot^2\theta\] \[\csc^2\theta\] \[\sec^2\theta\] \[\sin^2\theta\]

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by Brilliant Staff

Which of the following is equal to \(1-\sin^2\theta?\)

\[\cot^2\theta\] \[\sec^2\theta\] \[\csc^2\theta\] \[\cos^2\theta\]

Show explanation

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by Brilliant Staff

Which of the following is equal to \((1-\cos\theta)(1+\cos\theta)?\)

\[\cot^2\theta\] \[\csc^2\theta\] \[\sin^2\theta\] \[\cos^2\theta\]

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by Brilliant Staff

Which of the following is equal to \((\sin\theta-1)(\sin\theta+1)?\)

\[\sec^2\theta\] \[\cot^2\theta\] \[-\cos^2\theta\] \[-\csc^2\theta\]

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by Brilliant Staff

Which of the following is equal to \(\dfrac{\sec^2\theta}{\tan^2\theta+1}?\)

\[\frac{1}{4}\] \[1\] \[\sin^2\theta\] \[\cos^2\theta\]

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by Brilliant Staff

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