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  4. If ( cos (A-B)/ cos (A+B))=(8/3), then tan A ⋅ tan B is

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Q. If $\frac{\cos (A-B)}{\cos (A+B)}=\frac{8}{3}$, then $\tan A \cdot \tan B$ is

Trigonometry

Solution:

(i) Use componendo and dividendo theorem, i.e.,
$\frac{a}{b}=\frac{a+b}{a-b}$
(ii) Use the formula $\cos (A-B)$ and $\cos (A+B)$.
(iii) Take cross multiplication and find $\tan A+\tan B$.