Question

if cot A = 4/5 prove sin A + cos A/sin A - cos A = 9

Answer 1

cotA = 4/5

cosA/SinA = 4/5

So, cosA = 4 and sinA = 5

Now putting value in sinA + cosA/sinA - cosA

= 5 + 4/ 5- 4

= 9/1 = 9 = RHS

Answer 2

Answer:

Lets see…. You have given Cot A = 4/5.

Step-by-step explanation:

You have asked to prove that Sin A + Cos A / Sin A – Cos A = 9.

Let us see in Trignometry Cot A = 1 / Tan A.

And Tan A = Sin A / Cos A.

Now substituting values we get

Tan A = 1 / Cot A = 1 / 4 / 5 = 5 / 4.

Again we know that Tan A = Sin A / Cos A.

As Tan A = 5 / 4 so Sin A = 5 and Cos A = 4.

Now coming to proving side, we are given Sin A + Cos A / Sin A – Cos A = 9

L.H.S we get by substituting values of Sin A = 5 and Cos A = 4 in equation…

5 + 4 / 5 – 4 = 9 / 1 = 9 = R.H.S.