Proving Sum and Difference Trigonometric Identities Practice Problems Online

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 $\cos^2x+\cos^2y+\cos^2z?$

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}

Proving Sum and Difference Trigonometric Identities