Complete the identity.
-$$\frac { \sin ( \alpha - \beta ) } { \sin ( \alpha + \beta ) } = ?$$
A) $\frac { \tan \alpha \tan \beta - 1 } { \tan \alpha \tan \beta + 1 }$

B) $\frac { \tan \alpha - \tan \beta } { \tan \alpha + \tan \beta }$

C) -1

D) $\frac { \sin \alpha - \sin \beta } { \sin \alpha + \sin \beta }$

Question

Complete the identity.
-$$\frac { \sin ( \alpha - \beta ) } { \sin ( \alpha + \beta ) } = ?$$
A) $\frac { \tan \alpha \tan \beta - 1 } { \tan \alpha \tan \beta + 1 }$

B) $\frac { \tan \alpha - \tan \beta } { \tan \alpha + \tan \beta }$

C) -1

D) $\frac { \sin \alpha - \sin \beta } { \sin \alpha + \sin \beta }$

Quizplus · Accepted Answer

The identity $\frac { \sin ( \alpha - \beta ) } { \sin ( \alpha + \beta ) }$ simplifies to $\frac { \tan \alpha - \tan \beta } { \tan \alpha + \tan \beta }$ using the sine difference and sum formulas and dividing numerator and denominator by $\cos \alpha \cos \beta$.

Complete the Identity sin⁡(α−β)sin⁡(α+β)=?\frac { \sin ( \alpha - \beta ) } { \sin ( \alpha + \beta ) } = ?sin(α+β)sin(α−β)​=?

Complete the Identity $\frac { \sin ( \alpha - \beta ) } { \sin ( \alpha + \beta ) } = ?$