If sin A = 5/13. Find cos A, tan A, cosec A, sec A, cot A

 

sin A = 5/13

 

 (side opposite  to  ∠A)/Hypotenuse = 5/13

 ⇒ BC/AC = 5/13

 

Let

      BC = 5x

      AC = 13x

 

We find AB using Pythagoras Theore

Triangle ABC 13x 5x .jpg

 

In Δ ABC, using Pythagoras theorem

(Hypotenuse) 2 = (Height) 2 + (Base) 2

  AC 2 = AB 2 + BC 2

  (13x) 2 = AB 2 + (5x) 2

  169x 2 = AB 2 + 25x 2

  169x 2 – 25x 2 = AB 2

  144x 2 = AB 2

  AB 2 = 144x 2

  AB = √144x 2

  AB = √144 x

  AB = 12x

 

So, our triangle becomes

Triangle ABC 12x 13x 5x.jpg

 

Now, we find cos A & tan A

cos A tan A.jpg

 

Now, let us find cosec, cot and tan

cosec A sec A cot A.jpg

  1. Chapter 8 Class 10 Introduction to Trignometry
  2. Concept wise
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