Question

If tan A=7/12, what is cos A?

Answer 1

Given that tan(A) = 7/12, we can use the relationship between the tangent and cosine functions to find the value of cos(A).

tan(A) = sin(A) / cos(A)

So, dividing both sides by tan(A), we get:

tan(A) = sin(A) / cos(A)
=> cos(A) = sin(A) / tan(A)
=> cos(A) = 1 / (sqrt(1 + tan^2(A)))

Plugging in the value of tan(A) = 7/12:

cos(A) = 1 / (sqrt(1 + (7/12)^2))
=> cos(A) = 1 / (sqrt(1 + 49/144))
=> cos(A) = 1 / (sqrt(196/144))
=> cos(A) = 1 / (sqrt(196/144))
=> cos(A) = 1 / (sqrt(4/3))
=> cos(A) = sqrt(3/4)

So, cos(A) = sqrt(3/4).