Question

please answer quality answers will be marked as brainliest ​

Answer 1

Answer:

$\huge\bold\red{ANSWER}$

Step-by-step explanation:

$\blue{\bold{\underline{\underline{GIVEN :}}}}$

$\implies \sf \frac{x}{y}=\frac{cosA}{cosB} \\ \\ \implies \sf Asking\:to\:find\: \frac{xtanA+ytanB}{x+y}$

$\large{\underline{\rm{\red{SOLUTION :}}}}$

$\implies \sf \frac{x}{cosA}=\frac{y}{cosB}=K$

$\implies \sf x=kcosA\\ \\ y=kcosB$

$\implies \sf \frac{xtanA+ytanB}{x+y}=\frac{(kcosA)\frac{sinA}{cosA}+(kcosB)\frac{sinB}{cosB}}{kcosA+kcosB}$

                        $\sf =\frac{k(sinA+sinB)}{k(cosA+cosB)}$

                        $\sf =\frac{2 sin[\frac{A+B}{2}]cos[\frac{A-B}{2}]}{2 cos[\frac{A+B}{2}]cos[\frac{A-B}{2}]}$

                        $\sf =tan[\frac{A+B}{2}]$