Quotient identities and reciprocal identities

Examples
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Lessons
  1. Simplify expressions
    1. cos⁡x⋅tan⁡x+sin⁡x2tan⁡x\frac{\cos x \cdot \tan x + \sin x}{2 \tan x }
    2. cot⁡x(sin⁡x+tan⁡x)csc⁡x+cot⁡x \frac{\cot x (\sin x + \tan x)}{ \csc x + \cot x}
    3. cos⁡x+cot⁡x1+csc⁡x\frac{\cos x + \cot x}{1 + \csc x}
  2. Prove identities
    1. sin⁡A+tan⁡A1+cos⁡A=1cot⁡A \frac{ \sin A + \tan A}{ 1 + \cos A} = \frac{1}{ \cot A}
    2. cot⁡x−11−tan⁡x=csc⁡xsec⁡x \frac{\cot x - 1}{1 - \tan x} = \frac{\csc x}{\sec x}