complete the identity sinq / cosq + cosq / sinq =
I'm not sure I'm coming up with
1 + cot q
Use the Quotient Identities. (The "q" hints at that, too.) The Quotient Identities are the rules for tangent and cotangent.
yes that's what I did I just wasn't sure if I came up with the correct answer ?
The Quotient Identities are:
tanx = sinx / cosx
cotx = cosx / sinx
All you have to do is substitute those into your equation.
To complete the given identity:
We can start by writing the individual terms with a common denominator, which is sinq * cosq:
sinq / cosq + cosq / sinq
Now, let's find a common denominator by multiplying the first term by sinq/sinq and the second term by cosq/cosq:
(sinq * sinq) / (sinq * cosq) + (cosq * cosq) / (sinq * cosq)
Using the definition of trigonometric identities (sin^2 q + cos^2 q = 1), we can simplify the numerator:
1 + cos^2 q
Now, we can rewrite cos^2 q as 1 - sin^2 q (using the identity cos^2 q = 1 - sin^2 q):
1 + (1 - sin^2 q)
Finally, simplifying the expression further:
1 + 1 - sin^2 q
2 - sin^2 q
So, the simplified form of the given identity is 2 - sin^2 q.