Question

If tan A = 15/7, find the value of cosec A + cot A​

Answer 1

Given:-

• tanA = $\sf{\dfrac{15}{7}}$

To find:-

The value of cosecA and cotA

Solution:-

We know,

TanA = $\sf{\dfrac{Perpendicular}{Base}}$

Therefore,

$\sf{\dfrac{15}{7} = \dfrac{Perpendicular}{Base}}$

So now,

We have,

Perpendicular = 15

Base = 7

According to pythagoras theorem,

$\sf{(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2}$

= $\sf{Hypotenuse = \sqrt{(15)^2 + (7)^2}}$

= $\sf{Hypotenuse = \sqrt{225 + 49}}$

= $\sf{Hypotenuse = \sqrt{274}}$

= $\sf{Hypotenuse = 16.6\:units}$

Now,

CosecA = $\sf{\dfrac{Hypotenuse}{Perpendicular}}$

CosecA = $\sf{\dfrac{16.6}{15}}$

CotA = $\sf{\dfrac{Base}{Perpendicular}}$

CotA = $\sf{\dfrac{7}{15}}$

Now,

CosecA + CotA

= $\sf{\dfrac{16.6}{15} + \dfrac{7}{15}}$

= $\sf{\dfrac{16.6+7}{15}}$

= $\sf{\dfrac{31.6}{15}}$

Therefore the value of CosecA + CotA is $\sf{\dfrac{31.6}{15}}$

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Points to remember!!!

• $\sf{SinA = \dfrac{Perpendicular}{Hypotenuse}}$

• $\sf{CosA = \dfrac{Base}{Hypotenuse}}$

• $\sf{TanA = \dfrac{Perpendicular}{Base}}$

• $\sf{CosecA = \dfrac{Hypotenuse}{Perpendicular}}$

• $\sf{SecA = \dfrac{Hypotenuse}{Base}}$

• $\sf{CotA = \dfrac{Base}{Perpendicular}}$

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