Question

If SinA-xcosA=0, show that secA. cosecA=x+1/x​

Answer 1

$sina - xcosa = 0 \\ \implies \: sina = xcosa \\ \implies \: \frac{sina}{cosa} = x \\ \implies \: tana = x \\ so \: \: cota = \frac{1}{x} \\ now \: \: tana + cota = x + \frac{1}{x} \\ \implies \: \frac{sina}{cosa} + \frac{cosa}{sina} = x + \frac{1}{x} \\ \implies \: \frac{1}{sinacosa} = x + \frac{1}{x} \\ \implies \: secacoseca = x + \frac{1}{ x }$