Question

What is $\frac{\tan C}{\sin C}$ is equal to?

Answer 1

Relationship between trigonometric ratios:

As we know,

$\mathbf{tan}\mathbf{}\mathbf{C}\mathbf{=}\frac{\mathbf{sin}\mathbf{}\mathbf{C}}{\mathbf{cos}\mathbf{}\mathbf{C}}$

$$\begin{gathered} \therefore \frac{\tan C}{\sin C}=\frac{{\displaystyle \frac{\sin C}{\cos C}}}{\sin C} \\ =\frac{\sin C}{\cos C}\times \frac{1}{\sin C} \\ =\frac{1}{\cos C} \\ =\sec C\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{[}\mathbf{\because }\mathbf{}\frac{\mathbf{1}}{\mathbf{cos}\mathbf{}\mathbf{C}}\mathbf{=}\mathbf{sec}\mathbf{}\mathbf{C}\mathbf{]} \end{gathered}$$

Hence, the given expression $\frac{\mathbf{tan}\mathbf{}\mathbf{C}}{\mathbf{sin}\mathbf{}\mathbf{C}}$ is equal to $\mathbf{sec}\mathbf{}\mathbf{C}$