Pythagorean identities

Examples
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Lessons
  1. Use the unit circle to derive the Pythagorean Identity:
    cos2θ+^2 \theta + sin2θ=1^2 \theta = 1
  2. Simplify expressions:

    1. (sec2x−1)^2x -1) (cot2x)^2x)
    2. (1+sin⁡x)cos⁡x−cos⁡x1−sin⁡x \frac{(1+ \sin x )}{\cos x} - \frac{\cos x}{1 - \sin x}
  3. Prove identities
    1. sin⁡x1+cos⁡x+sin⁡x1−cos⁡x=2csc⁡x \frac{\sin x}{ 1 + \cos x} +\frac{\sin x}{1 - \cos x} = 2\csc x
    2. tan⁡x(csc⁡x+1)=cot⁡xcsc⁡x−1\tan x (\csc x + 1) = \frac{ \cot x}{ \csc x - 1}