**
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

**
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

Now, we find cos A & tan A

Now, let us find cosec, cot and tan