Question

Find dp/dq for p=(cos(q)-sin(q))/cos(q). [dp/dq=]

Answer 1

To find dp/dq for p=(cos(q)-sin(q))/cos(q), you can simplify the expression and then differentiate it with respect to q.

Step-by-step explanation:

To find ∂p/∂q for p = (cos(q)-sin(q))/cos(q), we can start by simplifying the expression:

p = (cos(q) - sin(q))/cos(q)

First, we can rewrite sin(q) as cos(π/2 - q) to use the cofunction identity:

p = (cos(q) - cos(π/2 - q))/cos(q)

Using the cosine difference identity, we can simplify the numerator:

p = (2sin((π/2 + q)/2)sin((π/2 - q)/2))/cos(q)

Next, we can use the quotient identity for cos(q) to simplify the expression:

p = (2sin((π/2 + q)/2)sin((π/2 - q)/2))/(cos^2(q) - sin^2(q))

Finally, we can simplify further:

p = (2sin((π/2 + q)/2)sin((π/2 - q)/2))/cos^2(q) - sin^2(q)

So, ∂p/∂q = (2cos((π/2 + q)/2)sin((π/2 - q)/2))/(cos^2(q) - sin^2(q))