Express cosA in terms of cotA
cotA = cosA/sinA
cosA = cotA/cscA
= cotA/√(1+cot^2 A)
To express cos(A) in terms of cot(A), we need to use the identity:
cot(A) = cos(A)/sin(A)
Starting with this identity, let's solve for cos(A):
Multiply both sides of the equation by sin(A):
cot(A) * sin(A) = cos(A)
Now, we replace cot(A) with cos(A)/sin(A):
cos(A)/sin(A) * sin(A) = cos(A)
Simplifying, the sin(A) terms cancel out:
cos(A) = cos(A)
Therefore, we see that cos(A) can be expressed as cos(A) when cot(A) = cos(A)/sin(A).
To express cosA in terms of cotA, we need to use the reciprocal trigonometric identity.
The reciprocal identity for cotangent (cot) is:
cotA = 1/tanA
Since tangent (tan) is the reciprocal of cosine (cos), we can express cotA in terms of cosA:
cotA = 1/cosA
To express cosA in terms of cotA, we can take the reciprocal of both sides:
1/cotA = cosA
Therefore, cosA can be expressed as 1/cotA.