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Proving Trigonometric Identities

Concept Quizzes

Proving Trigonometric Identities Warmup
Proving Trigonometric Identities
Advanced Proving Identities using Pythagorean
Proving Sum and Difference Trigonometric Identities

Challenge Quizzes

Proving Trigonometric Identities: Level 4 Challenges

Proving Sum and Difference Trigonometric Identities

Which of the following is equal to $\sin(x+y)\sin(x-y)?$

\sin2x

\sin(x^2-y^2)

\cos^2x-\cos^2y

\cos^2y-\cos^2x

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by Brilliant Staff

Which of the following is equal to $\displaystyle \frac{\sin x + \sin 3x}{\cos x - \cos 3x}?$

\cot 2x

\tan 2x

\tan x

\cot x

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by Brilliant Staff

If $x,y,z$ are the internal angles of a triangle, which of the following is equal to the sum $\sin x+\sin y+\sin z?$

0

\sin x\sin y\sin z

4\cos\frac{x}{2}\cos\frac{y}{2}\cos\frac{z}{2}

\frac{1}{4}\tan 2x\tan 2y\tan 2z

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Evaluate $\cos^2\theta+\cos^2\left(\theta+\frac{2}{3}\pi\right)+\cos^2\left(\theta-\frac{2}{3}\pi\right).$

0

\frac{1}{2}

1

\frac{3}{2}

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If $x,y,z$ are the internal angles of a triangle, which of the following is equal to the sum $\cos^2x+\cos^2y+\cos^2z?$

1-2\sin x\sin y\sin z

1-2\cos x\cos y\cos z

\tan 2x\tan 2y\tan 2z

-\cot\frac{x}{2}\cot\frac{y}{2}\cot\frac{z}{2}

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by Brilliant Staff

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