Question

Cot A - cot 2A = cosec 2A

Answer 1

Hello!

Cosec can be represented as csc in this problem.

Identities:

1.
`cot 2A` =
`(cos A)/(sin A)`

2.
`sin(A - 2A) = -cos(A)sin(2A) + cos(A)sin(2A)`

3.
`sin(A)= (1)/(csc(A))`

The variables A and 2A, can be changed to different variables.

`(cos A)/(sin A)` -
`(cos 2A)/(sin 2A)` =
`csc 2A` (Identity 1)

`(-cos(2A)sin(A) + cos(A)sin(2A))/((sin(2A)(sinA)) = csc 2A`

`(sin(-A + 2A) )/(sin(2A)sin(A))` =
`csc 2A` (Identity 2)

`(1)/(sin(2A))` =
`csc 2A` (Identity 3)

`((1)/(1))/(csc(2A))` =
`csc 2A` (Simplify)

`csc(2A) = csc(2A)`

The equation,
`cot A - cot 2A = cosec 2A`, is a true identity.