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Proving Trigonometric Identities

So, you've memorized your fundamental identities, but how can you prove the more obscure ones? See how to apply the basic building blocks of trig to understand deeper relationships.

Proving Sum and Difference Trigonometric Identities

         

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

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

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

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

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

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