Question

If 5 cot B = 12, then the value of cosec B + Sec B is ________. ​

Answer 1

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If , 5 cot B = 12 , then find the value of cosec B + sec B .

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★ Given :

• 5 cot B = 12

★ To Find :

• cosec B + sec B = ?

★ Answer :

Since ,

$\rm \: 5 \cot(b) = 12$

$\rm \: cot(b) = \dfrac{12}{5}$

$\rm \: \dfrac{base}{perpendicular} = \dfrac{12}{5}$

Consider a right angled triangle ,

in which ,

Base = 12x

Perpendicular = 5x

Using , Pythagoras Theorem ,

(Hypotenuse)² = (Base)² + (Perpendicular)²

(Hypotenuse)² = (12x)² + (5x)²

(Hypotenuse)² = 144x² + 25x²

$\rm \: hypotenuse \: = \sqrt{169 {x}^{2} }$

$\boxed{ \rm \: hypotenuse = 13x}$

Now , Finding the value of required term .

$\mapsto \rm \: cosec(b) + sec(b)$

$\implies \rm \: \frac{hypotenuse}{perpendicular} + \frac{hypotenuse}{base}$

$\implies \rm \: \frac{13x}{5x} + \frac{13x}{12x}$

$\implies \rm \: \frac{13x \times 12 + 13x \times 5}{12 \times 5x}$

$\implies \rm \: \frac{156x + 65x}{60x} \\ \\ \implies \: \frac{221 \cancel{x}}{60 \cancel{x}}$

$\implies \: \frac{221}{60}$

So ,

$\mapsto \boxed{ \rm \: cosec(b) + sec(b) = \frac{221}{60} }$

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★ Formula Used :

• $\sf \: cosec( \theta) = \frac{hypotenuse}{perpendicular}$
• $\sf \: sec( \theta) = \frac{hypotenuse}{base}$