1.

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

Answer»

Given:-

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}}

______________________________________

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}}

______________________________________


Discussion

No Comment Found

Related InterviewSolutions