Question

Prove
cot 2x + tan x = cosec 2x

Answer 1

cot 2x + tan x = cosec 2x

cosec 2x - cot 2x = tanx

LHS

= cosec(2x) - cot(2x)

= 1/sin(2x) - cos(2x)/sin(2x)

= 1/(2sin(x)cos(x)) - (cos²(x) - sin²(x))/(2sin(x)cos(x))

= (1 - cos²(x) + sin²(x)) / (2sin(x)cos(x))

= 2sin²(x) / (2sin(x)cos(x))

= sin(x) / cos(x)

= tan(x)

= RHS

Answer 2

Here is your answer ↑↑

Hope it's helpful for you....