Been 20 years since I've identified trig identities. We are stuck on a particular type and would appreciate some explanation. 1/sin(-x) * (1-cos^2x) that's cos(squared x) and 1+1/cos(-x) / -sinx-tanx
Because
This can be derived multiple ways...the most intuitive being
On the unit circle which has a radius of one any of the points on the circle have coordinates
So the distance from the origin to any point on the circle which I stated earlier is 1
So setting up the distance equation we have
Simplifying we get
Usually in trig classes this indentity is just taken to be true
First, convert everything to sines and cosines using the identities
Then, combine the fractions in the numerator and denominator, reduce, factor and cancel, and you should be left with if you do it right. When working this one, it may be helpful to observe that, since sine is an odd function and cosine is even,
If you have difficulty with the simplification, let us know.