Complete the identity.
-$\frac { \cos ( \alpha - \beta ) } { \cos \alpha \sin \beta } =$ ?
A) $\tan \alpha + \cot \beta$
B) $\tan \alpha + \cot \alpha$
C) $\tan \alpha + \tan \beta$
D) $\cot \beta + \tan \alpha \tan \beta$

Question

Quizplus · Accepted Answer

The identity can be derived by using the sum and difference formulas for cosine and the definitions of tangent and cotangent. Specifically, $\cos(\alpha - \beta) = \cos\alpha\cos\beta + \sin\alpha\sin\beta$. Dividing both sides by $\cos\alpha\sin\beta$, we get $\frac{\cos(\alpha - \beta)}{\cos\alpha\sin\beta} = \frac{\cos\alpha\cos\beta}{\cos\alpha\sin\beta} + \frac{\sin\alpha\sin\beta}{\cos\alpha\sin\beta} = \cot\beta + \tan\alpha$, which matches choice A.

Complete the Identity cos⁡(α−β)cos⁡αsin⁡β=\frac { \cos ( \alpha - \beta ) } { \cos \alpha \sin \beta } =cosαsinβcos(α−β)​=

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