Geometry

Proving Trigonometric Identities

Proving Sum and Difference Trigonometric Identities

         

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

Which of the following is equal to sinx+sin3xcosxcos3x?\displaystyle \frac{\sin x + \sin 3x}{\cos x - \cos 3x}?

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

Evaluate cos2θ+cos2(θ+23π)+cos2(θ23π).\cos^2\theta+\cos^2\left(\theta+\frac{2}{3}\pi\right)+\cos^2\left(\theta-\frac{2}{3}\pi\right).

If x,y,zx,y,z are the internal angles of a triangle, which of the following is equal to the sum cos2x+cos2y+cos2z?\cos^2x+\cos^2y+\cos^2z?

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