If cosec θ = , then the value of tan θ is 1. 12/5 2. 5/12 3. 5/13 4. 5/12

Let ABC be a right angle triangle with ∠B = 90° and ∠C = θ. By formula, cosec θ = Substituting values we get : Let AC = 13x and AB = 12x. In right angle triangle ABC, ⇒ AC 2 = AB 2 + BC 2 ⇒ (13x) 2 = (12x) 2 + BC 2 ⇒ 169x 2 = 144x 2 + BC 2 ⇒ BC 2 = 169x 2 - 144x 2 ⇒ BC 2 = 25x 2 ⇒ BC = . By formula, tan θ = . Hence, Option 1 is the correct option.

Mathematics

If cosec θ = $\dfrac{13}{12}$ , then the value of tan θ is
$\dfrac{12}{5}$
$\dfrac{5}{12}$
$\dfrac{5}{13}$
$\dfrac{5}{12}$

Trigonometrical Ratios

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Answer

Let ABC be a right angle triangle with ∠B = 90° and ∠C = θ.

If cosec θ = 13/12, then the value of tan θ is? Trigonometrical Ratios, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

By formula,

cosec θ = $\dfrac{\text{Hypotenuse}}{\text{Perpendicular}}$

Substituting values we get :

$\Rightarrow \dfrac{13}{12} = \dfrac{AC}{AB}$

Let AC = 13x and AB = 12x.

In right angle triangle ABC,

⇒ AC² = AB² + BC²

⇒ (13x)² = (12x)² + BC²

⇒ 169x² = 144x² + BC²

⇒ BC² = 169x² - 144x²

⇒ BC² = 25x²

⇒ BC = $\sqrt{25x^2} = 5x$ .

By formula,

tan θ = $\dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{AB}{BC} = \dfrac{12x}{5x} = \dfrac{12}{5}$ .

Hence, Option 1 is the correct option.

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Mathematics

If cosec θ = $\dfrac{13}{12}$ , then the value of tan θ is
$\dfrac{12}{5}$
$\dfrac{5}{12}$
$\dfrac{5}{13}$
$\dfrac{5}{12}$

Trigonometrical Ratios

Answer

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