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

Question

If ( cos (A-B)/ cos (A+B))=(8/3), then tan A ⋅ tan B is (A) (5/11) (B) (7/13) (C) (8/5) (D) (11/5)

Tardigrade Admin · Accepted Answer

(i) Use componendo and dividendo theorem, i.e., (a/b)=(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.

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

$\frac{5}{11}$

$\frac{7}{13}$

$\frac{8}{5}$

$\frac{11}{5}$

(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 $tan A + tan B$ .

Q. If cos(A+B)cos(A−B)​=38​, then tanA⋅tanB is

115​

137​

58​

511​