Prove cot 2x + tan x = cosec 2x

1.	Prove cot 2x + tan x = cosec 2x
Answer» 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»

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

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Prove cot 2x + tan x = cosec 2x

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