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

1 Answer
Jim H
Oct 1, 2015

See the explanation below.

Explanation:

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#

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