Question

Prove that the trigonometric ratios are same for the same angles

Answer 1

Answer:

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Answer 2

Answer:

Concept:

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). Trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle in geometry. As a result, trig ratios are evaluated in terms of sides and angles.

Step-by-step explanation:

As shown in the attached image,

$Consider \ \triangle P O Q \& \triangle M O N . \begin{aligned}&\angle P O Q=\angle M O N=\theta \\&\angle P Q O=\angle M N O=90^{\circ}\end{aligned} \triangle P O Q \sim \triangle M O N \quad (AAA similarity criterion)$

$\begin{gathered}\frac{P Q}{M N}=\frac{P O}{M O}=\frac{O Q}{O N} \\\frac{P Q}{M N}=\frac{P O}{M O} \\\frac{P Q}{P O}=\frac{M N}{M O} -- 1\end{gathered}$

$\triangle P O Q , =\quad \quad {S i n} \theta=\frac{\text { perpendicular }}{\text { hypoteneus }}=\frac{P Q}{P O} \triangle M O N , {\sin \theta}=\frac{M N}{M D} \\By eq 1, \quad \frac{P Q}{P O}=\frac{M N}{M O} \\ \sin \theta(\triangle P O Q)=\sin \theta(\triangle M O N)$

Hence proved that the trigonometric ratios are the same for the same angle.

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