Answer:
[tex]sec\ y = \frac{6}{b}[/tex]
Step-by-step explanation:
Given
[tex]sin\ y = \frac{a}{6}[/tex]
[tex]tan\ y = \frac{a}{b}[/tex]
Required
sec y
From trigonometry;
[tex]sec\ \theta = tan\ \theta\ /\ sin\ \theta[/tex]
Substitute y for θ
[tex]sec\ y= tan\ y\ /\ sin\ y[/tex]
Substitute values for tan y and sin y
sec y = a/b ÷ a/6
[tex]sec\ y= \frac{a}{b} /\ \frac{a}{6}[/tex]
[tex]sec\ y= \frac{a}{b} *\ \frac{6}{a}[/tex]
[tex]sec\ y= \frac{6 * a}{a *b}[/tex]
[tex]sec\ y= \frac{6 a}{ab}[/tex]
Divide numerator and denominator by a
[tex]sec\ y= \frac{6}{b}[/tex]
Hence, the value of sec y is
[tex]sec\ y= \frac{6}{b}[/tex]
