How do you prove the identity $(1-cos2x) / tanx = sin2x$ ?

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Answer 1 · 2015-10-01T01:21:13

See the explanation below.

Use one of the identities:

$cos2x = cos^2x-sin^2x$
$cos2x = 1-2sin^2x$
$cos2x = 2cos^2x-1$

Playing around with them on scratch paper (or thinking about them) will lead to using the second version.

$(1-cos2x) / tanx = (1-(1-2sin^2x))/tanx$

$= (2sin^2x)/(sinx/cosx)$

$= 2sin^2x * cosx/sinx$

$= 2sinxconsx$

$= sin2x$

How do you prove the identity (1-cos2x) / tanx = sin2x(1-cos2x) / tanx = sin2x?