Complete the identity.
-$$\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?$$
A) 0
B) $\tan ( 3 \theta ) \tan ( 6 \theta )$
C) $\cot ( 6 \theta )$
D) $- \tan ( 6 \theta )$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the trigonometric identity for the tangent of the sum of angles, specifically the formula for $\tan(x+y) = \frac{\sin(x+y)}{\cos(x+y)}$, and the sum-to-product identities. The correct simplification leads to $\tan(3\theta) \tan(6\theta)$, making option B the correct choice.

Complete the Identity cos⁡(3θ)−cos⁡(9θ)cos⁡(3θ)+cos⁡(9θ)=?\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?cos(3θ)+cos(9θ)cos(3θ)−cos(9θ)​=?

Complete the Identity $\frac { \cos ( 3 \theta ) - \cos ( 9 \theta ) } { \cos ( 3 \theta ) + \cos ( 9 \theta ) } = ?$