Home › Class 10 › Mathematics › Chapter 8 › Q2 Chapter 8 · Question 2 Show that tanA=sinAcosA\tan A=\frac{\sin A}{\cos A}tanA=cosAsinA. menu_book Back to Chapter Answer Direct Answer Since sinA=oppositehypotenuse\sin A=\frac{\text{opposite}}{\text{hypotenuse}}sinA=hypotenuseopposite and cosA=adjacenthypotenuse\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}cosA=hypotenuseadjacent, sinAcosA=oppositeadjacent=tanA\frac{\sin A}{\cos A}=\frac{\text{opposite}}{\text{adjacent}}=\tan AcosAsinA=adjacentopposite=tanA. Simple Explanation Divide sine by cosine; the hypotenuse cancels. Exam-Ready Structure Using definitions, sinAcosA=oppositehypotenuseadjacenthypotenuse=oppositeadjacent=tanA\frac{\sin A}{\cos A}=\frac{\frac{\text{opposite}}{\text{hypotenuse}}}{\frac{\text{adjacent}}{\text{hypotenuse}}}=\frac{\text{opposite}}{\text{adjacent}}=\tan AcosAsinA=hypotenuseadjacenthypotenuseopposite=adjacentopposite=tanA. Key Points Since sinA=oppositehypotenuse\sin A=\frac{\text{opposite}}{\text{hypotenuse}}sinA=hypotenuseopposite and cosA=adjacenthypotenuse\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}cosA=hypotenuseadjacent, sinAcosA=oppositeadjacent=tanA\frac{\sin A}{\cos A}=\frac{\text{opposite}}{\text{adjacent}}=\tan AcosAsinA=adjacentopposite=tanA. Related Questions Q3 Write the values of sin30∘\sin 30^\circsin30∘, cos60∘\cos 60^\circcos60∘, tan45∘\tan 45^\circtan45∘, and sec60∘\sec 60^\circsec60∘. arrow_forward Q4 State the trigonometric ratios of complementary angles. arrow_forward Report a mistake Previous Q1: Define the six trigonometric ratios for an acute angle $A$ in a right triangle. All questions Next Q3: Write the values of $\sin 30^\circ$, $\cos 60^\circ$, $\tan 45^\circ$, and $\sec 60^\circ$.