Question

In ∆ABC, if sin A = and tan A = , then what is cos A?

Answer 1

Complete Question:

In ∆ABC, if sin A = 4/5 and tan A = 4/3, then what is cos A?

Answer:

`cos A= (3)/(5)`

Step-by-step explanation:

Given

`sin A = 4/5`

`tan A = 4/3`

Required

`cos A`

In trigonometry;

`tanA = (sinA)/(cosA)`

Multiply both sides by cosA

`cos A * tanA = (sinA)/(cosA) * cos A`

`cos A * tanA = sinA`

Divide both sides by tanA

`(cos A * tanA)/(tanA) = (sinA)/(tanA)`

`cos A= (sinA)/(tanA)`

Substitute values for sinA and tanA

`cos A= (4/5)/(4/3)`

`cos A= (4)/(5) / (4)/(3)`

`cos A= (4)/(5) * (3)/(4)`

`cos A= (4 * 3)/(5 * 4)`

`cos A= (3)/(5)`