Answer:
[tex]\sec y=\dfrac{q}{r}[/tex]
Step-by-step explanation:
Given that,
[tex]\sin y=\dfrac{7}{q}[/tex]
and
[tex]\tan y=\dfrac{7}{r}[/tex]
We need to find the value of [tex]\sec y[/tex]. We know that,
[tex]\sec\theta=\dfrac{1}{\cos\theta}[/tex]
Also,
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}\\\\\cos\theta=\dfrac{\sin\theta}{\tan\theta}[/tex]
Substitute all the values,
[tex]\cos y=\dfrac{\dfrac{7}{q}}{\dfrac{7}{r}}\\\\=\dfrac{7}{q}\times \dfrac{r}{7}\\\\\cos y=\dfrac{r}{q}[/tex]
So,
[tex]\sec y=\dfrac{1}{\dfrac{r}{q}}\\\\\sec y=\dfrac{q}{r}[/tex]
So, the correct option is (a) i.e. [tex]\sec y=\dfrac{q}{r}[/tex].
