Question

if tanalpha tanB = 1, then the value of cos (alpha+Betta)is​

Answer 1

Answer:

The answer is 0

Step-by-step explanation:

Given   $\tan \alpha\tan\beta=1$

         $\Rightarrow \frac{\sin \alpha}{\cos\alpha}\times \frac{\sin\alpha}{\cos\beta}=1\\\Rightarrow \sin \alpha\sin\beta=\cos\alpha\cos\beta$...(1)

Thus  $\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\cos\beta$

                           $=\cos\alpha\cos\beta-\sin\alpha\sin\beta\\=0$, using (1)