How do you verify the identity $4 csc 2x = 2 csc^2x tan x$ ?

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Answer 1 · 2015-04-28T11:50:36

We will be using a Trigonometric identity to prove this-
$color(blue)(sin(2x) = 2sinxcosx$

The left hand side is $4csc2x$

$= 4/(sin2x)$ (Because $cscx = 1/sinx$ )

$= 4/(2sinxcosx)$

$= color(green)(2/(sinxcosx)$

The right hand side is $2 csc^2x tan x$

$= 2*(1/sin^2x)*(sinx/cosx)$ (Because $tanx = sinx/cosx$ )

$= color(green)(2/(sinxcosx)$

Hence proved.

How do you verify the identity 4 csc 2x = 2 csc^2x tan x4 csc 2x = 2 csc^2x tan x?