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Geometry

Proving Trigonometric Identities

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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