Hello!
Cosec can be represented as csc in this problem.
Identities:
1. [tex] cot 2A [/tex] = [tex] \frac{cos A}{sin A} [/tex]
2. [tex] sin(A - 2A) = -cos(A)sin(2A) + cos(A)sin(2A) [/tex]
3. [tex] sin(A)= \frac{1}{csc(A)} [/tex]
The variables A and 2A, can be changed to different variables.
[tex] \frac{cos A}{sin A} [/tex] - [tex] \frac{cos 2A}{sin 2A} [/tex] = [tex] csc 2A [/tex] (Identity 1)
[tex] \frac{-cos(2A)sin(A) + cos(A)sin(2A)}{(sin(2A)(sinA)} = csc 2A [/tex]
[tex] \frac{sin(-A + 2A) }{sin(2A)sin(A)} [/tex] = [tex] csc 2A [/tex] (Identity 2)
[tex] \frac{1}{sin(2A)} [/tex] = [tex] csc 2A [/tex] (Identity 3)
[tex] \frac{\frac{1}{1}}{csc(2A)} [/tex] = [tex] csc 2A [/tex] (Simplify)
[tex] csc(2A) = csc(2A) [/tex]
The equation, [tex] cot A - cot 2A = cosec 2A [/tex], is a true identity.
