Chapter 8 · Question 2

Show that $\tan A=\frac{\sin A}{\cos A}$ .

Answer Revealed

Direct Answer:

Since

\sin A=\frac{\text{opposite}}{\text{hypotenuse}}

and

\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}

\frac{\sin A}{\cos A}=\frac{\text{opposite}}{\text{adjacent}}=\tan A

Divide sine by cosine; the hypotenuse cancels.

Using definitions,

\frac{\sin A}{\cos A}=\frac{\frac{\text{opposite}}{\text{hypotenuse}}}{\frac{\text{adjacent}}{\text{hypotenuse}}}=\frac{\text{opposite}}{\text{adjacent}}=\tan A

Since $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$ , $\frac{\sin A}{\cos A}=\frac{\text{opposite}}{\text{adjacent}}=\tan A$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

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